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ENV 1991-3

TRAFFIC LOADS ON BRIDGES

BACKGROUND AND NOTES

FOR GUIDANCE

BACKGROUND

December 1994

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CONTENT

FOREWORD

CHAPTER 1 : TRAFFIC DATA

CHAPTER 2 : ASSESSMENT METHOD OF THE REAL TRAFFICEFFECTS ON BRIDGES

CHAPTER 3 : ASSESSMENT OF THE EC1.3 LOAD MODELS(CHARACTERISTIC VALUES)

CHAPTER 4 : REPRESENTATIVE VALUES OF THE ACTIONS DUETO ROAD TRAFFIC - GROUPS OF LOADS

CHAPTER 5 : LOAD MODELS FOR FATIGUE ASSESSMENTOF ROAD BRIDGES

ANNEX A : TRAFFIC EFFECTS ON ROAD BRIDGES ANDTARGET VALUES

ANNEX B : COMPARISON BETWEEN THE MAIN LOADING SYSTEMEFFECTS AND THE TARGET VALUES

ANNEX C : ELEMENTS FOR THE DEFINITION OF BRIDGE CLASSES

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FOREWORD

The redaction of an Eurocode related to the actions began in 1985. The work co-ordination was done by the Building Research Establishment (B.R.E.). In a first time itwas decided to only develop parts related to the actions most commonly applied onbuildings. However, a part related to the loads on bridges was rapidly needed.

Bridges are public structures that are rather systematically under the responsibilities ofpublic authorities. As the prescriptions of the European Directive 71 305 were usuallyapplicable on them, the creation of a specific organisation that would elaborate a normrelated to the loads was agreed.

For road bridges and footbridges a working group was appointed by the EEC. It wasconvened by M. Henri MATHIEU, General Engineer of the French Administration of« Ponts et Chaussées », and included representatives of the national authorities ofseveral countries members of the EEC. The first plenary meeting of this group was heldon the 10th and 11th of September 1987.

Several subgroups appointed made in order to conduct prenormative studies aboutseveral themes. The composition of these subgroups and their mission are gathered inTable 0.1.

The first technical results let appear new needs in the domain of prenormative research,so that, in 1990, the number and the composition of these subgroups was changed totake into account these new needs. The list and the composition of the subgroups at thedate of March 1990 are given in Table 0.2.

At the end of 1991, the redaction works of what is now called the Eurocode 1 Part 3(EC1.3) were transferred to the C.E.N. and allocated to two project-teams (PT6 for theloads on road bridges and footbridges, PT7 for loads on rail bridges). The compositionof PT6 is given in Table 0.3.

This document is intended to explain the method used to obtain the traffic load modelsgiven in EC1.3.

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Subgroup Nr. Members Associated experts1Definition of a set of referencebridges and of influence surfaces

Pr. CALGAROPr. KÖNIGM. MALAKATASM. EGGERMONT

M. PRATPr. SEDLACEK

2Definition of real traffic samples

Pr. KÖNIGPr. BRULSM. JACOBM. PAGE

Pr. SEDLACEK

3Definition and preliminarytreatment of exceptional loads

M. DE BUCKM. KANELAIDISM. EGGERMONTM. WEEDEN

4 et 7"Working Panel"Definition of the representativevaluesSimulations et comparisons

M. MATHIEUM. DE BUCKPr. SEDLACEKPr. CALGAROPr. SANPAOLESIM. DAWE

Pr. BRULSPr. KÖNIGMr. JACOBMr. PRATPr. NICOTERA

5Determination of the dynamiceffects of the traffic

Pr. NICOTERAPr. SEDLACEKM. ASTUDILLO

Pr. KÖNIG

6Determination of othercomponents of the traffic actions

M. GILLANDM. PFOHLM. O'CONNORM. MEHUE

M. VAABEN

Table 0.1 : Composition of the subgroups in 1988

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Subgroup Nr. Members Associated experts1Definition of a set of referencebridges and of influence surfaces

Pr. CALGAROPr. KÖNIGM. MALAKATASM. EGGERMONT

M. PRATPr. SEDLACEK

2Definition of real traffic samples

Pr. KÖNIGPr. BRULSM. JACOBM. PAGE

Pr. SEDLACEK

3Definition and preliminarytreatment of exceptional loads

M. DE BUCKM. KANELAIDISM. EGGERMONTM. WEEDEN

4"Working Panel"

M. MATHIEUM. DE BUCKPr. SEDLACEKPr. CALGAROPr. SANPAOLESIDr. FLINT

Pr. BRULSPr. KÖNIGMr. JACOBMr. PRATPr. MARTINEZ

5Determination of the dynamiceffects of the traffic

Pr. SEDLACEKPr. PETRANGELIPr. BRULSM. EYMARDM. ASTUDILLO

M. DROSNERM. JACOB

6Determination of othercomponents of the traffic actions

M. GILLANDM. PFOHLM. O'CONNORM. MEHUE

M. VAABENDr. FLINT

7Verifications for the fatigue

Pr. BRULSPr. SEDLACEKPr. SANPAOLESIM. JACOB

Pr. KÖNIGDr. FLINT

8Extrapolation methods and"target" values

M. JACOBPr. SEDLACEKPr. BRULSDr. FLINT

M. MERZENICHM. BEZ

9Safety and reliability problems

Dr. FLINTPr. SEDLACEKM. JACOBPr. BRULSPr. SANPAOLESI

Table 0.2 : Composition of the subgroups in March 1990

Official members of project team Nr.6 Associated expertsM. MATHIEU, ConvenorM. GULVANESSIAN, technical secretaryPr. BRULSDr. FLINTPr. SANPAOLESIPr. SEDLACEK

Pr. CALGAROMr. MERZENICHM. PRATM. CROCEM. JACOBMr. GILLAND

Table 0.3 : Composition of PT6 from 1992

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CHAPTER 1TRAFFIC DATA

The available traffic data provided by various countries have been gathered and analysedby subgroup Nr. 2 (see Foreword).

These data included :

- old data collected from 1977 to 1982 in France, Germany, Great Britain, Italy andThe Netherlands. These data were part of a C.E.C.A. research program on fatigue insteel bridges ;

- recent data mostly collected in 1986 and 1987 in several countries. Four countries(France, Germany, Italy and Spain) had full records of traffic on computer,including all the needed information about the axle weights of heavy vehicles, aboutthe spacing between axles and between vehicles, and about the length of thevehicles.

Most of the data were recorded on the "slow lane" of motorways or main roads (this lanesupports the heaviest traffic). The duration of the records varied from a few hours tomore than 800 hours.

The traffic data were mostly used to define two load systems : the main loading system(Load Model 1) and the complementary system consisting of a single axle (Load Model2). These models are described in chapter 3.

1.1 TRAFFIC COMPOSITION

Usually the observed medium flow of heavy vehicles varied from 2500 to 4500 vehiclesper day on the slow lane of motorways or of main roads, from 800 to 1500 per day onthe other roads. On the "express" lanes on motorways or on the carriageways ofsecondary roads, this medium flow dropped to 100 or 200 vehicles per day.

The distribution of the distance between lorries followed a "gamma" type law with amode between 20 and 100 m, a mean value that varies from 300 to more than 1000 m

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and a large variation coefficient (2 to 4). For memory, the variation coefficient is theratio of the standard deviation of the distribution over its mean value.

In order to analyse the composition of the traffic, four classes of vehicles were definedas follows :

- class 1 : double-axle vehicles ;- class 2 : rigid vehicles with more than two axles ;- class 3 : articulated vehicles ;- class 3 : draw bar vehicles.

Although the traffic composition is not identical from one European country to theother, the most frequent types of vehicles were the double-axle vehicles and thearticulated vehicles. The lorries with trailers were met most frequently in Germany.

The number of axles per vehicle, which depends on the constructor, varied widely, butthe histograms of their spacing showed three persistent modes with peak valuesparticularly constant :

- d = 1,30 m, corresponding to the double and triple axles with a very small standarddeviation,

- d = 3,20 m, corresponding to the tractor axles of the articulated lorries, with a smallstandard deviation,

- d = 5,40 m, corresponding to the other spacings but with a widely scattereddistribution.

1.2 - AXLE AND VEHICLE WEIGHTS

The value of the axle weight was very scattered, with an average value around 60 kN.But the maximum weight corresponding to a day time return period was much morestable from one location to the other. The Table I.1 shows the maximum weight per axletype, corresponding to a day time return period.

Singleaxles

Tandems Tridems

Value range (kN)of the maximum in a day

140 to 200 220 to 340 (*) 300 to 380

(*) Most of the values varied between 250 and 300 kN

Table I.1

The maximum value of the total weight of vehicles for a day time return period wasrather constant from one location to the other, mostly in a range 550 - 650 kN. All thestatistical distributions had two modes : the first one around 150 kN and the second one(corresponding to 20 or 30% of the lorries) around 400 kN.

Finally, and despite some variations in the result of the measurements from one countryto the other (these variations resulted mostly from the choice in traffic samples), it wasnoticed that the road traffic parameters were not so different, especially for themaximum daily values of the axle and vehicle weights.

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This is probably related to :- The fact that the various national lorries constructors make the same kind of

vehicles and export them widely in the European countries.- The fact that the transport companies try to load their vehicles as much as possible

in order to get lower costs.- The fact that the motorways and the roads mostly used by the heaviest vehicles are

used by a long distance traffic, which is going to be more and more international.

1.3 - CIRCULATION CONDITIONS OF THE VEHICLES

[To be developed]

1.4 - OTHER PARAMETERS ACTING UPON THE TRAFFIC

[To be developed]

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CHAPTER 2ASSESSMENT METHOD OF THE REALTRAFFIC EFFECTS ON BRIDGES

2.1 - THE STUDIED INFLUENCE SURFACES

Preliminary studies had been made to compare the various load systems of the existingEuropean codes. They had shown that all these systems had both qualities and failings.Therefore it was decided to build an original loading system that obeys to the followingrules :

a) Its effects had to reproduce very accurately (apart from a range factor) the totalutmost effects due to the actions of the real traffic (or stem from the chosenrepresentative values) for various forms and dimensions of the influence surfaces.

b) Its effects could not vary too much if the system only partially applies on therelevant influence surfaces, so that the worst loading case can be easily deternined.

c) Its application rules should be as simple and unambiguous as possible, either withcalculations made "by hand" or with softwares.

It was decided that the observed loads would apply to various theoretical influence linesand surfaces corresponding to :

- the longitudinal and transverse bending moment,- the torsion in beams,- the normal and shear forces in beams,- the concentrated efforts in transverse or cross beams.

We also studied the influence surfaces that depend on the longitudinal and transversebending moment in slabs (straight and skewed), but the calibration tests of the Eurocodeload system only focused on the influence surfaces of beams. These surfaces arerepresented in Figure 2.1.

Though it is not very significant for the studied problems, the influence surface a)(which depends on the normal force) allows to estimate the total load on part of thecarriageway; it is at least very simple to use.

The influence surface b) corresponds to the bending moment at mid-span of a simplysupported beam.

The influence surface c) corresponds to the maximum bending moment at mid-span of asymmetrical fixed beam with a variable moment of inertia. More precisely, in order toincrease the surface peak, we assumed that the ratio between the moments of inertia atmid-span and at the ends is very small. The variation law of the inertia I(x) was taken as:

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1 42

2I xK

x

L

x

L I( ) min= −

= with K

When x = 0, we notice that 1/I(x) = 0, which means that the ratio I

Imin

max is nil, i.e. that

the moment of inertia of the end cross sections is very large comparatively to themoment of inertia of the mid-span cross section.

The influence surface d) corresponds to the bending moment at the end of a fixed beamsimilar to the former one.

The influence surface e) corresponds to the shear force at mid-span of a simplysupported beam.

The influence surface f) corresponds to the torsion moment at mid-span of a simplysupported beam (positive part of the influence).

The influence surface g) corresponds to the application of a concentrated load on a crossbeam or a transverse beam.

In general, the chosen spans were the following ones :

L = 5, 10, 20, 50, 100, 200 m

The influence surface width was related to the number of notional lanes.

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EFFECT INFLUENCE SURFACEa) Normal forceN(x,y) = 10 < x < L0 < y < l

b) Bending moment

M(x,y) = x

20 < x < L/20 < y < l

c) Bending moment

M(x,y) = − +x

L

x

L

4

3

3

220 < x < L/20 < y < l

d) Bending moment

M(x,y) = 3 8 65

4

4

3

3

2

x

L

x

L

x

Lx− + −

0 < x < L0 < y < l

e) Shear force

V(x,y) = x

L if 0 < x < L/2

V(x,y) = x

L - 1 if L/2 < x < L

0 < y < l

f) TorsionT(x,y) = (1 - x/L)(y - l/2)L/2 < x < Ll/2 < y < l

g) Concentrated forcesQ(x,y) = 2x/L if y/x > L/lQ(x,y) = 2y/l if y/x < L/l0 < x < L/20 < y < l/2

Figure 2.1

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2.2 - EXPLOITATION OF THE ACTUAL TRAFFIC DATA

2.2.1 Definition of the problem

As previously explained, the real traffic records have been made on various locationsand during periods of time that varied from a few hours to more than 800 hours. We hadthen to define the utmost loads and the utmost effects of these loads in order to choosethe "characteristic values", that is the values corresponding to a certain probability ofnon-exceeding during the admitted reference period, which is 50 years.

It was decided to determine the "target values" of the traffic effects. These values haveto be reproduced in models, so that it corresponds to a probability of a 5% exceeding in50 years. The reasons are the following :

a) The traffic loads had to be studied in a similar way as nominal loads, that is loadshaving a small probability of exceedance during the reference period.

b) The probability for an exceedance of any irreversible serviceability limit stateduring the period of reference had to be limited, and the probability of severalexceedances had to be small.

The combination of both factors (reference period R and probability p) can be replacedby a single one which is the mean return period of a certain value. With the formervalues, this return period period is :

TR

p= = =50

0 05,1000 years

This return period may appear to be excessive in comparison with the lifetime of abridge generally considered. However, it has to be noticed that this notion has nophysical meaning for a variable action : it is only an invariant and helpful factor to relatea probability to a reference period.

Besides, to assess the actions of the atmospheric origin on buildings (wind and snow), itis referrred to a physical factor (for instance the height of snow on ground) with a meanreturn period of 50 years. But the consideration of a weather chart and of various factorsin the loading models leads, actually, to much higher real return periods, probably ofseveral centuries.

A mean return period of 50 years would not be enough because Load Model 1 (mainloading system) and Load Model 2 (single axle) are directly calibrated from theassessments of the loads effects (including the uncertainties of design). Besides, thevalues for the buildings loads, that are directly calculated as well, corresponds withoutany doubt to return periods of several centuries.

Finally, it is rational to think that the loads will increase in future.

A characteristic load is anyway supposed to represent a value with a small probability tobe reached or exceeded during the expected lifetime of the structure (100 years for

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bridges). Moreover, as explained later, the difference between the return period valuesof 1000 years or of 200 years is small because the distribution of the traffic utmosteffects is weakly scattered.

2.2.2 Extrapolation methods

A special subgroup worked on the various extrapolation methods that could be appliedto the utmost loads of the lorries and of their axles, to the total load on a lane length andto the utmost overall effects of the traffic.

Three methods were used, with some variations. The first one assumed that the queue ofthe distribution of local extrema follows a gaussian type law. In the second one, therecorded data distribution was substituted by a bi or tri-modal Gumbel law. The last oneassumed as well that the tail of the recorded data distribution followed a gaussian typelaw, but the extrapolations were based on an asymptotic distribution of the maxima.

With these methods, we successively studied the extrapolations about the utmost loadsof axles and lorries, the total utmost load on a single lane and the utmost actions due tothe traffic.

Table II.1 gives the extrapolated loads of axles and lorries for 20 weeks, 20 years and2000 years. These values result from the 3rd method (the two others giving similarresults).

Mean return period Type of load Extrapolated values20 weeks Single axle

TandemTridemGross weight

252332442690

20 week Single axleTandemTridemGross weight

273355479736

2000 years Single axleTandemTridemGross weight

295379517782

Table II.1

It has to be noted that, passing from a period of 20 weeks to 20 years, the valuesincrease of about 7 to 9%, and passing from 20 years to 2000 years, they increase againof 6 to 8%.

For the total effect of a free flowing traffic on one lane, the various methods gavehomogeneous results as well. For instance, Table II.2 gives the extrapolated values(average of the various methods) of the ratio, for various loaded lengths, of the totalload over the loaded length (in kN/m).

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L(m) Extrapolation to 20years

Extrapolation to 1000years

2050100200

45,6529,4320,4513,52

50,3733,0323,7315,70

Table II.2

This table shows that the extrapolation from 20 to 1000 years increases the value of theload per length unit of about 10 to 16%, depending on the loaded length.

Similar observations have been made for the effects of actions. For instance, Table II.3gives the extrapolated values of the equivalent distributed load (kN/m) that induces, fora simply supported beam and for a single loaded lane, the maximum bending moment atmid-span.

Spanlength

(m)

Mean returnperiod

20 weeks

Mean returnperiod

20 months

Mean returnperiod

20 years

Mean returnperiod

1000 years205075100150200

46,523,718,415,613,111,7

54,426,120,217,214,412,9

60,428,422,118,715,714,0

65,133,225,821,818,316,4

Table II.3

For these values, the increases are respectively about 10%, 9% and 17% when the meanreturn period passes from 20 weeks to 20 months, from 20 months to 20 years and from20 years to 1000 years.

From all the former results we can infer an average formula that gives the adjustmentfactor c depending on the mean return period T (in years) :

c = 1,05 + 0,116 log(T)

This factor is equal to 1 for a mean return period of about 20 weeks. It shows that, whenthe return period passes from 100 years to 1000 years, the values increase of about 9%.

Finally, any bridge can be subjected to various traffic situations : free flowing traffic,condensed traffic, traffic jam, special situations due to social demonstrations ("snail"operations), and so on. These situations have been extrapolated as well, mostly with asimulation software (based on the Monte-Carlo method) and starting from the observedtraffic on the A6 motorway near Auxerre.

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For instance Table II.4 shows, for a mean return period of 1000 years, the resultedvariations between the effects of a free flowing traffic, of a congested traffic with lightand heavy vehicles and of a congested traffic without any light vehicle. The valuescorrespond to an equivalent distributed load (in kN/m) that induces an utmost bendingmoment at mid-span of a simply supported beam.

Span length(m)

Free flowingtraffic

Congested trafficwith light vehicles

Congested trafficwithout light

vehicles2050100200

60,3434,2622,7617,70

51,4240,4535,7031,33

52,8742,4036,5033,63

Table II.4

2.2.3 Practical use of the results

All the studies about the extrapolation of the observed road traffic effects showed thatthe various methods were leading to practically equivalent results.

The first idea was to mix all the traffic records in order to get an "European sample", butsome of the extrapolation methods based on mathematical simulations of traffic neededa sample of homogeneous traffic. Starting from the fact that the traffic recorded on theA6 motorway near Auxerre was already an "European" traffic, it was decided that all thestatistical manipulations would be done with this single traffic.

Table A.1 of Annex A gives the values in the rough of the extrapolated values of thetraffic that has been recorded on the A6 motorway near Auxerre, either for free flowingtraffics and traffic jams. These effects are related to the various influence lanes andsurfaces defined in Figure 2.1.

During the measurements , the A6 motorway had 2 x 2 lanes numbered from 1 to 4 asrepresented in Figure 2.2 :- V1 refers to the traffic effects (in kN or kNm according to the cases) recorded on a"slow" lane.- V12 refers to the traffic effects simultaneously recorded on both lanes of the samecarriageway (a "slow" one and a "fast" one).- V14 refers to the traffic effects recorded on two "slow" lanes (in opposite direction).- V1234 refers to the traffic effects of all the traffic recorded on two carriageways.

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Figure 2.2

It is possible, by algebraic combinations (sums and differences) of these values, to getout the effects of any single lane.

For instance table A.2 of Annex A gives the extrapolated effects on some influencesurfaces of the traffic recorded on the RN 205 near Chamonix (symbol RN), on theBrohltal bridge in Germany and on the main road n°1 at Fiano Romano (symbol FN)between Roma and Firenze (Italy).

In particular we notice that the observed traffic on the slow lane of the Brohltal bridge ismore "aggressive" than the one observed on the slow lane of the A6 motorway. Besides,measurements were conducted in France on several locations and it was noted that thetraffic on the A6 motorway was not the heaviest one (see Table II.5).

SiteAll axles together Tandems Tridems Heavy vehicles

Numberof axlesper day

Dailymaximum

(1)

Numberof axlesper day

Dailymaximum

(1)

Numberof axlesper day

Dailymaximum

(1)

Numberof lorriesper day

Dailymaximum

(1)Chamonix (2)Garonor (3)Périphérique (4)Auxerre(5)Angers (6)

52251159325323104424757

155195210195160

38310161880844485

245290290305245

651489

1098961335

365320360390300

12043686807626301272

570560610630490

(1) Weights in kN.(2) RN205 between France and Italy, slow lane.(3) A1 motorway Paris - Lille, slow lane.

(4) Boulevard périphérique of Paris, lane n°2.(5) A6 motorway, slow lane.(6) RN23 near Angers, slow lane.

Table II.5 - Traffic characteristics on some French locations

2.3 DEFINITION OF THE "TARGET" EFFECTS

2.3.1 Dynamic effects of the road traffic (for flowing traffic only)

The problems related to the dynamic amplification of the road traffic effects have beenstudied by a particular subgroup (subgroup n°5).

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It was first decided that the real traffic records included some kind of dynamic effectwhich could be characterised with a factor equal to 1,10.

AACHEN and PARIS (LCPC) conducted many numerical simulations that consideredthe dynamic behaviour of the vehicles and of the bridges, and which were based onsome hypotheses about the roughness quality of the carriageway. For the evaluation ofthe characteristic load values, it was finally decided to consider an average roughnessand, for spans shorter than 15 m, local irregularities represented by a 30 mm thick plankthat can be, for instance, a located default of the carriageway surface or the missing of acarriageway joint element.

Noting :- Estat the static effect of the recorded traffic,- Edyn the calculated dynamic effect of the traffic,- ϕcalib the global dynamic amplification factor that results from the numerical

simulations,- ϕlocal the complementary amplification factor related to the local effects,

Table II.6 gives in short the formulae used to determine the "target" values.

Type oftraffic

Numberof lanes

Length ofthe

influenceline

Dynamic effect Edyn

Congested traffic(or traffic jam)

1 All spansEdyn =

Estat

1 10, x 1,10 = Estat

2 and 4 All spansEdyn =

Estat

1 10, x 1,00 = 0,90 x Estat

Free flowingtraffic

All lanes L > 15 mEdyn =

Estat

1 10, ϕcalib

All lanes L ≤ 15 m Edyn = Estat

1 10, ϕcalibϕlocal

Table II.6

To be noted : the factor ϕcalib represents the dynamic amplification of the consideredeffect and depends, among others, on the span length and on the type of influencesurface under consideration. It is evaluated by a statistical comparison with the staticeffect ; hence the maximum of the dynamic effect does not necessarily correspond to themaximum of the static effect.

That is the reason why the "target" values of the traffic effects have been determined foreach influence surface and each action effect, by directly considering the results ofparticular dynamic calculations.

For information and in order to have a rough idea, Figures 2.3 and 2.4 give an averagevalue of the dynamic magnification factors ϕcalib and ϕlocal, but these graphs have notbeen directly exploited, as we just said.

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a) One loaded lane b) Two and four loaded lanes

Figure 2.3 : Values of ϕϕϕϕcalib

Figure 2.4 : Values of ϕϕϕϕlocal

2.3.2 The loading patterns on the lanes

In order to determine the "target" values used for the calibration of the Eurocode loadingsystem, it was necessary to define loading patterns on the different lanes of a bridge.

First several authors independently studied the effect values that should reproduce thefuture European load system by considering various situations (scenarios), that meanscombinations of various traffics depending on the location of the lanes and the numberof them. This first approach of the patterns was later more precisely defined to get thepropositions given in short in Table II.7.

For the definition of the typical traffics :- A6 represents the traffic recorded on the A6 motorway near Auxerre ;- all the action effects have been extrapolated except the ones related to some lanes in

the proposition from PISA ;- "d" represents the conventional distance between two lorries to simulate a traffic

jam situation : it is systematically equal to 5 m ;- the term "congested" traffic has been chosen to represent (with some ambiguity)

various situations like traffic jam, a jam with successive movements of starting andstopping, or even a displacement at low speed.

The "congested" traffic has been considered either as a flowing traffic at very low speedor by simulation (random distribution of lorries and cars) in conditions estimated similaras a flowing traffic.

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Traffictype

Numberof lanes

Code LIEGE PARIS PISA AACHEN

Freeflowing

1 F1 A6 slow lane25% of lorries

A6recorded traffic

(slow lane)

A6 slow lanerecorded traffic

A6 slow lane100% of lorries

V = 60 - 80 kmh2 F2 2x(A6 slow lane)

25% of lorries2x(A6 - V1+V2)recorded traffic

1st lane:same as the former

2nd lane:A6 - Daily

maximum of the 1st

lane

1st lane:same as the former

2nd lane:A6 - slow lane

32,2% of lorriesV = 80 kmh

3 F3 1st and 2nd lanes :same as the former

ones3rd lane :A6 - Daily

maximum of the2nd lane

4 F4 2x(A6 - V1+V2)(10% of lorries)

1st, 2nd and 3rd

lanes :same as the former

ones4th lane :

A6 2nd lanedaily average

1st and 4th lanes:A6 slow lane

32,3% of lorries2ndand 3rd lanes :

A6 2nd lane9,2% of lorries

V = 10 kmhConges-

-ted1 C1 Maximum of :

- A6 slow lane100% of lorries

d = 5 m- A6 traffic jam

with 25% oflorries

A6100% of lorries

d = 5 m

A6 slow lane100% of lorries

d = 5 m

A6 slow lane100% of lorries

V = 10 - 20 kmh

2 C2 2x(A6 traffic jam)25% of lorries

d = 5 m

1st lane :same as the first one

2nd lane:F1

1st lane :same as the former

one2nd lane :

Maximum of :- A6 daily max.- medium traffic

jam with cars3 C3 1st and 2nd lanes :

same as the formerones

3rd lane :F2 - F1

1st and 2nd lanes :same as the former

ones3rd lane :

A6 slow laneDaily maximum

4 C4 4x(A6 slow lane)10% of lorries

d = 5 m

1st, 2nd and 3rd

lanes :same as the former

ones4th lane :

F2 - F1

1st, 2nd and 3rd

lanes :same as the former

ones4th lane :

A6 2nd lanedaily average

Table II.7 : Definition of the traffic types

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As can be seen the adopted processes in these propositions were deterministic (besides,it was the only ones that could be used considering our time constraint) and they wereconsidered as sufficient at this step. It is obvious that adaptations should be fitted forbridges with lighter traffic.

In short, considering that all the points of view were interesting, it has been decided todefine a single set of "target values" of the actions, after a few numerical corrections :

- starting from the envelope of all the results related to a free flowing traffic (thatincludes the dynamic amplification) for short and medium span lengths (up to about50 or 70 m),

- starting from the average value of all the results related to the situations withcongested traffic for long span lengths,

- by smoothing some irregularities mainly due to the lack of results for some spanlengths.

Finally, it appeared that the "target values" corresponding to very short spans (1 to 10 m)were not satisfactory, especially for the local effects. Specific studies leaded to correctthem by increasing them.

The influence lines and surfaces used to calculate the effects of the loading pattern aredefined in Table II.8 and Figure 2.5.

Nr. ofinfluence line

Nature of the influence line

I1 Maximum bending moment at mid-span of a simply supported beam.I2 Maximum bending moment at mid-span of a double fixed beam with an

inertia that strongly varies between mid-span and the ends.I3 Maximum bending moment on support of the former double fixed

beam.I4 Minimum shear force at mid-span of a simply supported beam.I5 Maximum shear force at mid-span of a simply supported beam.I6 Total load.I7 Minimum bending moment at mid-span of the first of the two spans of a

continuous beam (the second span only is loaded).I8 Maximum bending moment at mid-span of the first span of the former

continuous beam.I9 Bending moment on central support of the former continuous beam.

Table II.8 - Considered influence lines and surfaces

-21-

Figure 2.5 : Schematic representation of the influence lines and surfaces

Tables A.3 to A.6 of Annex A give successively, for 1, 2, 3 and 4 loaded lanes :- the envelope values and the mean values (dynamic magnification included) of theeffects of the free flowing traffic (if relevant) ;- the envelope values and the mean values of the congested traffic effects ;- the "target" values accepted according to what has been said previously.

When 3 or 4 lanes are loaded the effects calculated by integrating situations ofcongested traffic on the first or on the two first lanes are dominating. This is the reasonwhy the results corresponding to a free flowing traffic do not appear in these tables.

-22-

CHAPTER 3ASSESSMENT OF THE EC1.3 LOAD MODELS

(CHARACTERISTIC VALUES)

EC1.3 defines four loads models. The first one is the main model ; it is defined andcalibrated according to a scientific process roughly described hereafter. Model n°2 is amodel that complements the former, well adapted for some local verifications. Modelsn° 3 and 4 respectively correspond to situations with abnormal vehicles and a crowd ona deck bridge. They are used, in a particular project, only if explicitely required by theclient.

3.1 - GENERAL PRINCIPLES FOR THE MAIN MODEL CALIBRATION

From the very beginning, the aim of the works was to find a model that would includethe dynamic amplification with simultaneous concentrated and distributed loads, so thatthe general verifications and the local verifications could be simultaneously examined.The minimum intensity of the distributed load has been set to 2,5 kN/m2 on the basis ofexisting national standards. The calibration tests of the models later confirmed thisvalue.

The calibration tests have been carried out with methods of the operational research.The notation is :

* F(L) is the representative function of the effects of the load model to be calibrated,corresponding to the influence surfaces defined in the former chapter ;

* G(L) is the "target function" issued from the "target values" calculated for the sameeffects ;

* L is a length factor related to the studied influence line or surface.

For a given « segmentation » (?) of the influence line length, we note dk the elementarygap between Fk and Gk at the point k, defined by :

dF

Gkk

k= − =1 k 1,2,...n

and we introduce the following functions :

d MaxF

G

d

nk

k

kmax

( )= − =1 d m

Σ

The optimisation method consists in finding, for various models that depends on variousfactors, the function F so that :

* dm is minimum,* dmax is minimum as well,

* dmax and dm are minimum and F

Gk

k≥ r with r = 1 or 0,95.

-23-

A lot of calculations have been carried out with various laws for the concentrated andfor the distributed loads, on the influence lines basis that are described in Table II.8(Chapter 2). The results of these calculations are detailed hereafter.

3.2 - DEFINITION AND CALIBRATION OF THE MAIN LOADING SYSTEM

The calibration of the main loading system was progressively carried out, starting fromlane n°1 (main lane), then by successively adding lane n°2 and, simultaneously, lanesn°3 and 4.

3.2.1 Study of a model for lane 1

The calibration test of a model on lane n°1 showed that :- the introduction of more than two concentrated loads was superfluous because it did

not really improve the precision of the result,- a constant value of the uniformly distributed load, compared with decreasing

functions of the loaded length, reduced the precision of the results, with noticeablegaps on the unsafe side.

After this first calibration, two optimal solutions for the main lane loading wereidentified:

a) Solution n° 1 : one single concentrated load P1 = 400 kN for a loaded length L > 3m, and a uniformly distributed load following the law :

pL

= +30160

(kN / m)

b) Solution n°2 : two concentrated loads P1 = P2 = 185 kN, with a gap of 1,0 m, anda distributed load following the law :

pL

= +29 3375 6

,,

(kN / m)

In theses formulae, L is the loaded length.

Actually the first solution was rapidly set aside because to study the local effects withone single concentrated load was irrealistic.

3.2.2 Study of a model for both lanes 1 and 2

The analysis done on two lanes led to the following conclusions :

a) Concentrated load : the calibration study confirmed that it was not necessary toconsider more than two loads on the main lane ; more, concentrated loads on thesecond lane that are geometrically similar to the loads on the main lane (but withlower intensity) led for both lanes to more precise results than during the calibrationwith only the first lane loaded.

-24-

b) Uniformly distributed load (UDL system) : the study confirmed that a law that issimply decreasing with the loaded length was well adequate, for the second as forthe first lane.

c) The second lane did not change much the results of the model calibration on themain lane.

One possible solution, among the ones that offer the best numerical precision, isrepresented in Figure 3.1.

Figure 3.1

3.2.3 Study of a model for 4 lanes

The calibration tests of the model on 4 lanes led to adopt :- two concentrated loads of 435 kN each, with a gap of 1 m,- one distributed load equal to :

pL

= +

≥1 977 29 3375 6

, ,,

kN / m for L 3m.

Considering the loading method of the two first lanes, two concentrated loads of 150 kNand one uniformly distributed load equal to :

pL

= +ΦΗ ΙΚ0 56 29 3375 6

, ,,

kN / m

had to be dispatched on lanes 3 and 4.

3.2.4 Definition of the final load model

The solution described in the former section has been progressively changed. Theprecision of the "target" values of the actions has been slightly decreased in order thatthe final load model appears to be of very simple use and applicable in practice withoutambiguity.

-25-

There was a problem in the choice of the factor L ; one marking point of this"simplicity" was in the choice of a load density with an intensity that was independent ofthe loaded length. A new calibration test gave the model of Figure 3.2.

Figure 3.2

More studies about the influence lines and surfaces with a length smaller than 5 m led toincrease the intensity of the concentrated loads on the second lane, to correlativelydecrease the intensity of the distributed load on the same lane and to remove theconcentrated loads after the third lane. Besides, the distance between concentrated loadsin lanes n°1 and 3 was increased up to 1,20 m. This value seemed to fit better the realspacing between two axles of lorries, although the concentrated loads were not initiallysupposed to represent the axles of real vehicles.

The basic values of the finally adopted model are represented on the sketch of Figure3.3.

Figure 3.3 : Final main loading system

3.3 - DETAILED STATEMENT OF THE MAIN LOADING SYSTEM

3.3.1 Definition of the loadable length

-26-

For the sake of simplicity, it has been admitted since the very beginning that theloadable width of a deck was equal to the net width of the carriageway, measuredbetween the kerbs when they are higher than 100 mm ("boxed" value) or between theinner limits of relevant road restraint systems. It does not a priori include the distancebetween restraint systems or kerbs of central reservation.

3.3.2 Definition of the lanes

Considering that, in congested traffic situations, vehicles can drive close to the eachother, it has been admitted that the loads resulting from the calibration tests should applyon strips of 3 m wide. So are defined the so-called "notional lanes" of 3 m wide, that areindependent of the marker strips on the road surface.

These notional lanes can be located anywhere on the drivable surface : the number ofnotional lanes is thus usually calculated as the integer part of the division by 3 of thetotal loadable width (w). In case of bridges which loadable width is between 5,40 m and6,00 m, two lanes with a reduced width of w/2 are considered ; in case of loadable widthnarrower than 5,40 m (for instance an insertion lane on motorway), only one notionallane is considered.

3.3.3 Contact area of wheel loads

A detailed study of the local loads transmitted to the carriageway by heavy vehiclewheels has been carried out by M. PRAT in November 1989.

Two main tyre architectures are used : the diagonal frames used for planes andagricultural tractors and the radial frames for most part of the road vehicles. The roadloads on bridges are only concerned with the radial framed tyres ; their particularity isthat, by crushing, they only can get a longitudinal deformation (Figure 3.4).

Figure 3.4

-27-

The load only applies on a reduced and constantly changing zone of the pavement, andthe average pressure "p" on road is equal to the inflating pressure "pg" increased with thestructural tyre reaction, which is weak. The heavy load print is noticeably a rectanglewhose transverse dimension "b" is constant.

If we admit p = pg we can deduce from the possible tyre crushing f = R - Rf the

longitudinal dimensions a f R f= −2 2( ) of the corresponding contact areas (R is the

tyre radius when unloaded and Rf the tyre radius under maximum load).

Φrim

(inch)

D = 2Runloaded

tyre(mm)

Radius Rloaded

tyre(mm)

S(mm)

H/S b(mm)

aMax(mm)

Use

19,5 1098 494 477 0,65 470 480 Road20 1348 611 412 412 570 Road/

track24 1257 570 338 0,65 338 527 Road/

track15 934 420 278 278 420 Trailer25 1744 795 671 671 716 Mobile

crane

Table III.1 - Radial framed tyres for industrial vehicles

We notice that the contact areas on road are rather square and that, anyway, whenloaded, the transverse dimensions are less than or equal to the longitudinal dimensions.Another remarkable detail about the contact dimensions is that the road carriers havebeen saying for some time that they preferred unique wide tyres comparatively to the oldtwinned tyres that are still in use for the site lorries and some trailor axles. Theadvantages of wide tyres are obvious considering :

- safety : the vehicle mass centre is lowered, the chock absorbing effect is improved,the loads are better distributed, the load volume is bigger, no bursting risk anymoredue to the frequent difference in pressure between the twin tyres,

- the saving of tyres : less non-suspended masses,- the consumption : less driving resistance, tyres with suppler sides,- the carriageway damaging : less aggressive slipping, etc.

The contact area of wide tyres on the bridge structure extrados is calculated from atransverse dimension of 400 mm in average and a longitudinal length in dynamicsituation a bit longer than the transverse dimension.

In order to see how the phenomena are related one to each other, the following formulagives the axle load P as a function (here linear) of the pressure « p » for a given speedand a contact surface a bit bigger than 400 x 400 mm2.

P = 22(p + 0,7) < 140 kN

This kind of wide tyres is already in use on most of the heavy industrial vehicles andmight be generalised. The bridge designer must be aware of this fact and must take into

-28-

account the corresponding contact surface type in his calculations (including thepunching).

3.3.4 Description of the final main loading system (Load Model 1)

The final main loading system is represented in Figure 3.5.

Location Tandem system UDL system

Axle loads Qik (kN) qik (or qrk) (kN/m2)

Lane 1 300 9Lane 2 200 2.5Lane 3 100 2.5

Other lanes 0 2.5Remaining area

(qrk)0 2.5

Figure 3.5 : Main Loading System

-29-

NoteThe loads applied on bridge decks are distributed at the carriageway level oncontact surfaces whose geometry depends on the used tyre type. But actually theload diffuses in the bridge mass and structurally acts at the middle plane level.Hence the active zone of the load distribution is bigger than the contact surface.

Studies carried out in the USA in particular have shown that the pressures due tohigh loads are a decreasing function of the depth inside the slab, and aredistributed with an homothetia ratio of 1/1.

But it is important to notice that the pressure under the tyre is not alwaysuniformly distributed. During accidental situations such as a hard breaking, aslipping, a partial loss of contact of a wheel, or the beginning of an hydroplaningphenomenon, concentrations of pressure appear under some particular areas ofthe tyre and transmit in a harder way the load to the middle plane of the deck(concrete or steel) slab.

Loads can then be distributed on one third of the contact surface and diffuse inconcrete following an oblique line near the vertical line.

The application rules for this system are the following :

1) For each individual verification, the number of lanes to be loaded, their location onthe carriageway and their numbering (in decreasing order with the aggressiveness) arechosen in order that the model effects are the most adverse.

2) When the carriageway consists of two separate parts on two independent decks, eachpart is considered as a single carriageway : separate numbering is then used for thedesign of the lanes on each deck. However, if the two decks are supported by the samepiers and/or abutments, one single numbering for the two parts together is considered todesign these piers and/or abutments.

3) For each individual verification and on each notional lane, the load model should beapplied on such a length and so longitudinally located that the most adverse effect isobtained, as far as this is compatible with the following conditions :

* notional lanes must be considered with their full width,* only complete tandem systems shall be considered,* any residual area width can be chosen ; particularly it may be the part that gives rise

to the most adverse effect on a given influence surface.

4) The calibration of the main loading system has been carried out with the effects of aquite "heavy" traffic. Nevertheless, if we consider an actual bridge with a lighter trafficon it, a loading class may be attributed to him thanks adjustment factors on concentratedloads (factors α Q ) and on distributed loads (factors α q ).

3.3.5 Comparison between the main loading system effects and the "target" values

-30-

The values resulting from this comparison are given in Table B.1 of Annex B to thisbackground document. They give rise to a direct comparison between the main loadingsystem effects with the "target" values corresponding to the various influence linesdescribed in Figure 2.2 (chapter 2) for one, two and four loaded lanes (the "target"values come from Table A.3, A.4 and A.6 of Annex A).

We notice that the two series of values usually correctly match together. However thesytem effects noticeably deviate from the "target" values for some influence lines andfor some span lengths.

The recorded differences between the "target" values" and the values calculated from themodel for the I1 to I3 and I7 to I9 influence lines are graphically represented hereafter.

-31-

a) Influence line I1 (bending moment at mid-span of a simply supported beam)

0

20000

40000

60000

80000

100000

120000

140000

160000

180000

0 50 100 150 200

Target values

Computed values

Influence line I1 - Lane 1

0

50000

100000

150000

200000

250000

0 50 100 150 200

Target values

Computed values

Influence line I1 - Lanes 1+2

0

50000

100000

150000

200000

250000

300000

0 20 40 60 80 100 120 140 160 180 200

Target values

Computed values

Influence line I1 - Lanes 1+2+3+4

For this influence line, we notice a good matching, whatever the number of lanes can be,between the target values and the values calculated from the model ; these last ones aresmaller than the former ones.

-32-

b) Influence line I2 (bending moment at mid-span of a double fixed beam)

0

5000

10000

15000

20000

25000

30000

35000

40000

0 50 100 150 200

Target values

Computed values

Influence line I2 - Lane 1

0

10000

20000

30000

40000

50000

60000

0 20 40 60 80 100 120 140 160 180 200

Target values

Computed values

Influence line I2 - Lanes 1+2

0

10000

20000

30000

40000

50000

60000

70000

0 20 40 60 80 100 120 140 160 180 200

Target values

Computed values

I2 influence line - Lanes 1+2+3+4

The biggest differences are obtained with this influence line. The values obtained fromthe model are bigger than the calibration values for one and two loaded lanes. Thesedeviations are indicated in Table III.2.

Span Lane 1 Lanes 1+250 m100 m150 m200 m

29%18%12%9%

27%11%9%9%

Table III.2

-33-

c) Influence line I3 (maximum bending moment on support of a double fixed beam)

0

20000

40000

60000

80000

100000

120000

140000

0 50 100 150 200

Target values

Computed values

Influence line I3 - Lane 1

0

20000

40000

60000

80000

100000

120000

140000

160000

180000

200000

0 50 100 150 200

Target values

Computed values

Influence line I3 - Lanes 1+2

0

50000

100000

150000

200000

250000

0 50 100 150 200

Target values

Computed values

Influence line I3 - Lanes 1+2+3+4

The values computed from the model match good with the calibration values for oneloaded lane, and are smaller for two and more loaded lanes

-34-

d) Influence line I7 (minimum bending moment at mid-span of the first span of adouble span continuous beam)

0

5000

10000

15000

20000

25000

30000

35000

40000

0 50 100 150 200

Target values

Computed values

Influence line I7 - Lane 1

0

10000

20000

30000

40000

50000

60000

0 20 40 60 80 100 120 140 160 180 200

Target values

Computed values

Influence line I7 - Lanes 1+2

0

10000

20000

30000

40000

50000

60000

70000

80000

0 50 100 150 200

Target values

Computed values

Influence line I7 - Lanes 1+2+3+4

We can only notice that the values computed from the model are bigger than thecalibration values for two loaded lanes and a 200 m long span (deviation equal to 6%).

-35-

e) Influence line I8 (maximum bending moment at mid-span of the first span of adouble span continuous beam)

0

20000

40000

60000

80000

100000

120000

140000

0 50 100 150 200

Target values

Computed values

Influence line I8 - Lane 1

0

20000

40000

60000

80000

100000

120000

140000

160000

180000

0 20 40 60 80 100 120 140 160 180 200

Target values

Computed values

Influence line I8 - Lanes 1+2

0

50000

100000

150000

200000

250000

0 50 100 150 200

Target values

Computed values

Influence line I8 - Lanes 1+2+3+4

We notice some "adverse" deviations for one and two loaded lanes. In the first case, themaximum deviation is 24% at 50 m, but is only 8% at 100 m. In the second case, thedeviation is 16% at 50 m, 6% at 100 m, 3% at 150 m and 1% at 200 m.

-36-

f) Influence line I9 (bending moment on central support of a double span continuousbeam)

0

20000

40000

60000

80000

100000

120000

140000

160000

180000

0 50 100 150 200

Target values

Computed values

Influence line I9 - Lane 1

0

20000

40000

60000

80000

100000

120000

140000

160000

180000

200000

0 50 100 150 200

valeurs cibles

valeurs calculées

Influence line I9 - Lanes 1+2

0

50000

100000

150000

200000

250000

0 15

30

45

60

75

90

10

5

12

0

13

5

15

0

16

5

18

0

19

5

Target values

Computed values

Influence line I9 - Lanes 1+2+3+4

For this influence line the computed values are equivalent to or smaller than thecalibration values.

-37-

3.3.6 Definition of model n°2

The tandem systems of the main model do not cover all the local effects of vehicles ofvarious configurations. Therefore, for some local verifications (in particular in case oforthotropic slabs), the main loading model is completed with a loading system (LoadModel 2) that allows to take into account other contact surfaces than the onescorresponding to wide tyres (in case of double wheels) and to correct the effects of LoadModel 1 for short influence lines. It consists of a single axle corresponding to a load of400 kN (boxed value) to which can be applied an adjustment factor βQ depending on theclass of the expected traffic for a particular project (Figure 3.6).

Figure 3.6 - Load Model 2

3.4 - LOAD MODELS 3 AND 4

3.4.1 The Load Model 3

The Load Model 3 consists of a set of standardised vehicles and is intended to cover theeffects of special conveys. It results from a synthesis (carried out by subgroup Nr. 3 - seethe Foreword) dealing with the foreseen dispositions in the actual national codes. Thismodel is taken into account only when required by the client. The characteristics of thevarious vehicles are given in table III.3 and the contact area of the wheels are indicatedin Figure 3.7.

-38-

Figure 3.7

The application rules concerning special vehicles on the carriageway are detailed in theEC1.3.

-39-

Total load Composition Nomenclature600 kN 600/150

900 kN 900/150

1200 kN 1200/150

1200/200

1500 kN 1500/150

1500/200

1800 kN 1800/150

1800/200

2400 kN 2400/200

2400/240

2400/200/200

3000 kN 3000/200

3000/240

3000/200/200

3600 kN 3600/200

3600/240

3600/200/200

Table III.3 - Classes of special vehicles

3.4.2 The Load Model 4

The Load Model 4 consists of an uniformly distributed density of 5 kN/m2. This load isintended to represent the effect of a crowd, including the dynamic amplification. It isapplicable, when specified by the client, on the whole deck, including the centralreservation if relevant.

This system is intended for some structures made in town area. The load intensity hasbeen defined with reference to the existing national norms. But the system is dominatingonly above some dimensions of the structure.

-40-

3.5 - LOADS ON FOOTWAYS

The loads on footways are defined in section 5 of EC1.3 (see chapter 6 of thisbackground document). They are represented by an uniformly distributed density whichcharacteristic value is 5 kN/m2 ; this value was defined by referring to the existingnational norms as well.

3.6 - THE HORIZONTAL FORCES

3.6.1 Braking and acceleration forces

The braking or acceleration forces are taken as a longitudinal force acting at thecarriageway level. Their characteristic value, limited to 800 kN, is calculated as afraction of the total maximum vertical loads of the main loading system to be applied onlane Nr. 1, as follows :

Qlk = 0,6αQ1(2Q1k) + 0,10αq1 q1k wl L

180 αQ1 kN ≤ Qlk ≤ 800 kN

where :- L is the length of the deck or of the part under consideration- 2Q1k is the weight of both the axles of the tandem system placed on lane Nr. 1 (if L > 1,2m)- q1k is the density of the uniformly distributed load on lane Nr. 1- wl is the width (3m) of lane Nr.1- αQ1 and αq1 are the adjustment factors depending on the loading class.

This force intensity derives from a study carried out at AACHEN, using a simplifiedmodel based on the following hypotheses (these hypotheses have been confirmed bytests conducted in Switzerland) :

- a set of n identical lorries is considered with the same spacing, crossing the bridgein convoy with the same speed before braking than the first vehicle,

- the reaction time (the period of time between the braking of two consecutivelorries), is taken as the ratio of the distance between lorries over their initial speed(consequently the number of vehicles that brake simultaneously reaches a limit),

- the braking force of a lorry is proportional to its weight, with a factor that variesfrom 0,6 to 1 according to the type of lorry and its actual load,

- the dynamic interaction lorry-bridge is taken into account thanks to rheologicmodels of spring, chock absorber and friction element in parallel.

Various simulations were carried out with various parameters and they induced a firstproposition giving the braking force as a function of the span length (Figure 3.8).

-41-

Figure 3.8 : Braking force (first proposition)

The proposed formula in the EC1.3 derives from the former proposition. But it seemeduseful to relate the braking forces to the vertical load to be applied on the deck.

3.6.2 Centrifugal forces

EC1.3 defines the characteristic value of a transverse force acting on the carriagewaylevel radially to the axis of the carriageway, as indicated in Table III.4.

Qtk = 0,2 Qv (kN) if r < 200 m

QQ

rtkv= 40 (kN)

if 200 1500≤ ≤r m

Qtk = 0 if r > 1500 mr is the horizontal curvature radius of the deck centrelineQv is the maximum total weight of vertical loads of the main loadingsystem.

Table III.4

These formulae derive from the equation :

QV Q

grtv=

2

where V is the vehicle speed (in m/s), Qv is the corresponding vertical force and g =9,81m/s2.

The value of Qtk corresponds to a speed of about 70 km/h. This speed has been chosenbecause the centrifugal force mainly depends on heavy vehicles. Individual cars do notgive rise to significant centrifugal effects.

-42-

CHAPTER 4REPRESENTATIVE VALUES OF THE ACTIONSDUE TO ROAD TRAFFIC - GROUPS OF LOADS

The various representative values of loads defined in the Eurocode 1.1 chapter 6 are :* the characteristic values (described in chapter 3 of this document) for the ultimate

limit states. Where these values are exceeded, irreversible consequences will result ;* the infrequent values ;* the frequent values ;* the quasi-permanent values.

Infrequent values have been required by drafters of EC2.2 (part "Bridges"). Theycorrespond to a mean return period period of one year. They seem to be intended forverifications concerning serviceability limit states that are close to the limit ofreversibility of the effects.

Frequent values correspond to a mean return period of one week. They only concernLoad Model 1 (main loading system) and Load Model 2 (single axle).

Quasi-permanent values of the actions due to the road traffic are usually null. In case ofbridges that support a heavy and continuous traffic a non null quasi-permanent value ofthe uniformly distributed load of the main loading system can be considered with aprobable uniform distribution in the transverse direction.

4.1 - CALIBRATION OF THE INFREQUENT AND FREQUENT VALUES OFTHE LOAD MODELS

Various simulations have been carried out to evaluate, on the basis of the theoreticalinfluence surfaces defined in chapter 2 of this document, the effects of the trafficcorresponding to a mean return period of one week to one year and by considering, asfor the characteristic values, loading scenarios of the carriageway. For indication, thescenarios resulting from the various propositions for two lanes are given in Table IV.1.

Although the loading hypothesis of the lanes are completely different, the results of thevarious extrapolation exercises are quite homogeneous and it was possible to state somevalues directly attributed to the groups of loads defined below.

-43-

FREQUENT VALUES INFREQUENT VALUESLane 1 Lane 2 Lane 1 Lane 2

Aachen Free flowing trafficA6 slow lane32% lorriesextrapolated to 1 week

Free flowing trafficA6 slow lane9% lorriesextrapolated to 1 week

Free flowing trafficA6 slow lane32% lorriesextrapolated to 1 year

Free flowing trafficA6 slow lane9% lorriesextrapolated to 1 year

Liège Free flowing trafficA6 slow lane25% lorriesextrapolated to 1 week

Free flowing trafficA6 slow lane25% lorriesextrapolated to 1 week

Free flowing trafficA6 slow lane25% lorriesextrapolated to 1 year

Free flowing trafficA6 slow lane25% lorriesextrapolated to 1 year

FNP(*) Congested traffic100% lorries(d = 5 m)extrapolated to 1 week

Night traffic60% lorriesextrapolated to 1 week

Day traffic30% lorriesextrapolated to 1 week

Night traffic60% lorriesextrapolated to 1 week

Day traffic30% lorriesextrapolated to 1 week

Congested traffic100% lorries(d = 5 m)extrapolated to 1 year

Night traffic60% lorriesextrapolated to 1 year

Day traffic30% lorriesextrapolated to 1 year

Night traffic60% lorriesextrapolated to 1 year

Day traffic30% lorriesextrapolated to 1 year

Paris Congested trafficslow lane A6extrapolated to 1 week

Free flowing trafficslow lane A6Weekly maximum

Congested trafficslow lane A6extrapolated to 1 year

Tafic fluideslow lane A6extrapolated to 1 year

Pisa Free flowing trafficSlow lane A6Weekly maximum

Congested trafficSlow lane A6Weekly maximumwith short distances(20 m)

Free flowing trafficFast lane A6Daily average

Congested trafficSlow lane A6Daily average

Free flowing trafficSlow lane A6extrapolation to 1 year

Congested trafficSlow lane A6swithout carsextrapolated to 1 year

Free flowing trafficFast lane A6Daily maximum

Congested trafficMax of :- Slow lane A6daily maximum- Fast lane A6daily maximum

(*) Flint, Neill and Partners

Table IV.1 : Hypotheses of lane loading

4.2 - DEFINITION OF GROUPS OF LOADS

In order to make easier the assessment of design combinations for bridges, some of theaction components have been gathered. Five groups of loads have thus be defined asindicated in Table IV.2.

-44-

CARRIAGEWAY FOOTWAYS ANDCYCLE TRACKS

Load type Vertical forces Horizontal forces Vertical forces onlyLoad system Main loading

systemSpecialvehicles

Crowd loading Braking andacceleration

forces

Centrifugalforces

Uniformly distributedload

gr1 Characte-ristic values

Reduced value2,5 kN/m2

gr2 (*) Frequentvalues

Characte-ristic values

Characte-ristic values

Groupsof loads

gr3 Characteristic values

gr4 Characte-ristic values

Characteristic values

gr5 (**) Characte-ristic values

(*) Although the simultaneity of two variable actions with their characteristic value is unlikely, this groupof loads has been proposed as a simplification, as far as it is clear that the consequences for the design arevery slight.(**) Special dispositions about the simultaneity of special vehicles with other loads on carriageway areconsidered in the EC1.3

The cases with double border designate the dominant actions.

Table IV.2 : Definition of infrequent and frequent valuesfor the groups of loads

The factors that define the "infrequent" values (ψ'1) and frequent values (ψ1) related tothe former groups (boxed values) are given in Table IV.3. It was agreed that ψ1 and ψ'1values, defined for the dominant action for each group, would be applied to allcomponents of the group.

Group of loads ψψψψ'1 ψψψψ1gr1

Tandem systemDistributed load

Single axle (Load Model 2)gr2gr3gr4gr5

0,800,800,80

00,800,801,00

0,750,400,75

0000

Horizontal forces 0 0

Table IV.4 : ψψψψ factors for road bridges

-45-

CHAPTER 5LOAD MODELS FOR FATIGUE ASSESSMENT

OF ROAD BRIDGES

5.1 - GENERAL

Questions related to fatigue verifications have been considered after the definition of thecharacteristic load models. However it was admitted that they only concern steel bridgesor composite steel concrete bridges and the models described below have been definedfrom this angle. Truly it is not possible to calibrate a fatigue model if the associatedverification rules are not taken into account. But when this part of the Eurocode hasbeen drafted, Parts 2 of the main structural Eurocodes were not yet available. We hadthen to refer to the most usual practice, and therefore to the practice of fatigue design forsteel bridges.

Five models numbered 1 to 5 have been defined for various uses, considering thatEurocode 1.3 should give :

- one or more rather "pessimistic" models to rapidly identify in what parts of astructure a problem of fatigue could appear,

- one or more models to perform common verifications in a manner as simple aspossible,

- one or more models to perform "accurate" verifications.

The two first models come from the first class, model Nr. 3 is from the second class andmodels Nr. 4 and 5 are from the last one. It was agreed that calibrations of designstrengths would lead to satisfactory verifications by using the models selected in eachdesign Eurocode.

5.2 - FATIGUE LOAD MODELS 1 AND 2

Fatigue Load Model 1 derives from the characteristic main loading system : each axleload is equal to 0,7 Qik and the value of the uniformly distributed loads is equal to 0,3qik (on notional lanes) or to 0,3 qrk on the remaining area.

This model determines a maximum and a minimum stress for a particular verification.

Fatigue Load Model 2 consists of a set of five lorries, called « frequent lorries », whichgeometrical and weight characteristics are given in Figure 5.1.

-46-

Lorry types Axle spacing(m)

Frequent axleweigth (kN)

4.5 90190

4.201.30

80140140

3.205.201.301.30

90180120120120

3.406.001.80

90190140140

4.803.604.401.30

90180120110110

Figure 5.1 : Definition of frequent lorries

Fatigue Load Model 2 determines the maximum and minimum stresses that result fromone of these lorries travelling on the slow lane of the bridge under consideration.

Models 1 and 2 are both intended to be used to check whether the fatigue lifetime maybe considered as unlimited by reference to S-N curves that have a constant amplitudefatigue limit. Actually, only the S-N curves of the EC3 (related to frame steels) have gotsuch a limit (Figure 5.2) corresponding to 5.106 cycles.

Figure 5.2 - Example of S-N curves related to normal stress

-47-

Thus, if the stress range that result from a single application of Fatigue Load Models 1and/or 2 are less than the point of the S-N curves of abscissa N = 5.106, we thenconsider that there is no way to get a fatigue ultimate limit state for the considereddetail. This implies that these both models have been calibrated with enough pessimism,so that their effects cover the effects of actual traffic.

Initially, the main loading system with frequent values was intended to used as FatigueLoad Model 1, but calibration exercises showed that it was too pessimistic because itresulted from consideration of heavy traffic situations and was based on loads recordedon the A6 motorway ; this model was not comparable with Fatigue Load Model 2calibrated by taking into account some resistance crireria.

That is the reason why it effectively derives from the main loading system, but withadjustment factors smaller than the ones related to the frequent values. Nevertheless thismodel is still relatively pessimistic, especially in some cases of small influence surfaces(local effects) because concentrated forces are then critical.

Fatigue Load Model 2 was intended to correct relevant faults resulting from the use ofthe previous one in case of short influence lines. "Frequent" lorries are normallycalibrated to cover 99% of the damages due to free flowing traffic, such as the onerecorded in Auxerre.

However it has to be noticed that :- only S-N curves related to frame steels have got a constant amplitude fatigue limit

and that, consequently, Fatigue Load Models 1 and 2 should not be used in thescope of the rules defined in EC2.2 ;

- calibration tests did not precisely show whenever each model had to be used,considering that Model 1 may be used for large loaded surfaces ;

- when using a constant amplitude fatigue limit, obscure discontinuities may occur inthe design of the fatigue lifetime issued from the Eurocodes for similar structures.

For all these reasons it seems that Fatigue Load Models 1 and 2 will not be used often inthe future, even if EC2.2 refers to a model similar to Model 1 (frequent load model) inorder to cover the cracking and the non-linearity of stresses in concrete with partialprestressing.

5.3 FATIGUE LOAD MODEL 3

Fatigue Load Model 3 is intended for common verifications without, if possible, anycalculations of damaging with, for instance, the Palmgren-Miner law. On one hand itstems from the existing models in national standards and, on the other hand, from theverification principles that have been agreed for the railway steel bridges.

The starting idea was to get a "fatigue convoy" so that, after a single transit of the modelalong the bridge and after a numerical adjustment with relevant factors, a single stressvariation could be calculated.

5.3.1 Calibration procedure of a fatigue convoy

-48-

In a first step, a series of life-times is computed on the basis of Miner's rule withCASTOR (LCPC) programme, and for the class of detail Nr. 36 in order to obtain anumerical realistic set of life-times.

These life-times were determined both for long and short span lengths by considering :- a set of 64 influence areas of stresses in joints belonging to 9 real bridges,- a set of 8 short influence areas of pyramidal shape.

The actual bridges considered in this study have 2, 3 or 4 lanes ; their span lengths varyfrom 22 to 102 m (see Annex A) and the decks are designed with 2 or 4 longitudinalbeams. The stress variations correspond to the crossing of the continuous beams by thetraffic.

For short span lengths, typical influence areas are considered, corresponding, forexample, to the stress in bottom flange of a transverse beam (Figure 5.3).

Figure 5.3

The corresponding data for these influence areas (short span lengths only) are :- the distance between two successive transverse beams, noted L/2, with L =3,4,5,6,7,8,9,10 metres ;- the maximum stress magnitude (MPa/kN) on the axis of the lanes, noted S (= 0,10 -0,12 - 0,15) ;- a constant spacing of 8 m between the longitudinal beams.

In fact, the very short influence lines have no physical meaning, but they permit to checkthe stability of the calibrated fatigue model. Two typical real traffics are considered :

- the traffic recorded in Auxerre on the slow lanes of the motorway (lanes 1 or 4) andin the fast lanes (lanes 2 or 3) ;- the traffic recorded on National Road Nr. 23 (2 lanes) near Angers (France), whichrepresents a typical highway traffic of medium intensity.

In a first step, a conventional fatigue convoy was considered. It was made of two tandemsystems spaced of 5, 6 or 7 m. Each tandem system had two axles of 75 kN each, inorder to remain always in the part of S-N curves with a slope of -1/5.

-49-

After the calculation of the various life-times, the number nS of applications of thefatigue model was determined, so as to obtain the same life-times for the same influenceareas. The results were reported in diagrams with :

- as abscissa log(LT) (LT = life-time, measured with the corresponding number ofload applications) ;

- as ordinate log(10-6.nS).

A linear regression was made in order to obtain a relation between the two parameters asfollows :

log (10 .n ) = A log(LT) + B-6S

and the accuracy of the regression is checked by considering the correlation coefficient.

log(10-6.nS) = A log(DL) + B

5.3.2 Numerical results

The following developments are based on the consideration of a particular S-N curve.For other S-N curves, the results might be slightly different.

The results of the calibration showed a linear regression of good quality and that therewas no significant difference between the three distances of tandems. In Table V.1 nS.100

represents the number of applications of the fatigue model corresponding to a design lifeof 100 years and ρ represents the correlation coefficient between the computed life-times from real traffic data and from the application of the fatigue model.

-50-

Distance between tandems 5 m 6 m 7 m

10-6.nS.100 ρ 10-6.nS.100 ρ 10-6.nS.100 ρ

Long influence lines andAuxerre traffic

368.13 0.945 388.87 0.947 412.57 0.949

Long influence lines andAngers traffic

41.84 0.953 45.49 0.954 49.60 0.955

Semi-local influence linesand Auxerre traffic

203.05 0.894 203.05 0.894 203.05 0.894

Local influence lines andAuxerre traffic

340.88 0.964 340.88 0.964 340.88 0.964

Table V.1

It has to be noticed that even for semi-local and local influence lines, the distancebetween tandems has no influence for the bridges under consideration.

It was proposed to take into account a fixed value for the tandem spacing, equal to 6 m,and to adopt the following mean values for 10-6.nS.100 , associated to axles of 75 kN, tocharacterise the two traffics :

- 10-6.nS.100 = 310 for Auxerre traffic,- 10-6.nS.100 = 45 for Angers traffic.

The scatter of the results by comparison to the 10-6.nS.100 values proposed above may becovered by considering, instead of 10-6.nS.100, the following value, noted 10-6.n*S.100

such that :

n * = n 10S.100 S.100k.dm×

where dm is the average absolute deviation between the computed life-times and theregression line and k is a factor to be fixed in relation with γSd and γm-factors, whichhave to cover other uncertainties (including the unification of nS.100).

The average absolute deviation dm is equal to 0.22.106 for Auxerre traffic and 0.175.106

for Angers traffic.

With these values the number of applications n*S.100 corresponding to a 75 kN axleconvoy and for a 100 years life-time is equal to :

* 514,5.106 for the Auxerre traffic (that means more than 108),* 67,3.106 for the Angers traffic.

These numbers are represented on the S-N curve of Figure 5.4.

-51-

Figure 5.4

5.3.3 Principle of the verifications

The adopted principle of verification for the calibration tests is described below. Theextreme stresses (maximum and minimum) resulting from the passage of the fatigueconvoy along the bridge are calculated in order to evaluate a stress range :

∆σLM LM LMMax Min= −σ σ

This stress range multiplied by a dynamic magnification factor ϕfat (given in figure 5.5)and a load factor λe gives :

∆σ ∆σfat e fat LM= λ ϕ. .

Figure 5.5 - Dynamic magnification factor for fatigue

The stress range ∆σfat is nominally compared to the value ∆σ2 of the S-N curve (Figure5.3). Considering this verification method, the factor λe is the product of three factors :

λe = λ1.λ2.λ3

* λ1 is related to the annual traffic volume,* λ2 is related to the expected life-time of the bridge under consideration,* λ3 is related to the effects of several lanes.

If we consider the value ∆σ2 corresponding to 2.106 cycles, we notice that the axleweight of the reference convoy (75 kN) should be multiplied by :

-52-

*∆σ∆σ

∆σ∆σ

2

1

1

0

1 3 1 55

2

100

52 471× =

×

=/ /

, for the Auxerre traffic,

* ∆σ∆σ

∆σ∆σ

2

1

16

1 3 1 5

67 3 10

5

2

67 3

52 283×

×=

×

=( , )

,,

/ /

for the Angers traffic

5.3.4 Justification of the accepted fatigue model

Fatigue Load Model 3 of the EC1.3 is represented in figure 5.6.

Figure 5.6 - Fatigue Load Model 3 of EC1.3

It consists of four axles of 120 kN each. Each axle has got two wheels which contactarea is a square of 0,40 x 0,40 m.

As said before the choice of the axle load is conventional as the factor λe has to beadjusted in order the justifications can be referred to a particular stress range of theconventional S-N curve (∆σ2 to 106 cycles).

If then this value and the axle load of the EC1.3 fatigue model are accepted, thereference convoy effects have to be counterbalanced with another factor :

4 75

4 1200 625

××

= ,

Therefore the EC1.3 fatigue convoy load has to be multiplied by :* 2,471 x 0,625 = 1,544 for the Auxerre traffic* 2,283 x 0,625 = 1,427 for the Angers traffic.

A total equivalent load of lorries in an actual traffic can besides be designed with theformula :

Qn Q

nei i

i=

ΣΣ

55

where ni is the number of lorries with a total load Qi. For the Auxerre traffic, Qe = 420kN and for the Angers traffic, Qe = 298 kN.

The calibration tests carried out at SETRA showed that the factor λ1 could be taken as :

λ10

5480

= ×KN

N

Qobs e

-53-

where K is a constant factor, N0 is the number of reference lorries per year in the slowlane and Nobs is the total number of lorries observed per year in the slow lane.

This formula has got two unknown factors, K and N0. However only the ratio K

N05

is

deterministic. If we take a priori N0 = 106 the factor λ2 can be identified to the factorsexplained above :

* Auxerre traffic :Nobs = 106, Qe = 420 kN, λe = 0,875 K = 1,544, hence K = 1,765* Angers traffic :Nobs = 0,87 x 106, Qe = 296 kN, λe = 0,604 K = 1,427,hence K = 2,363.

According to the precision of the fatigue assessments, an average value of K seemsconvenient :

K=2

Thus with the accepted verification method we obtain for λ1 :

λ1 2 = ×N Qobs e

10 48065

For λ2 :

λ 2

1 5

100=

LT /

(LT in years).

For a life-time of 100 years λ2 = 1.

Finally, the calibration tests showed that the significant loads related to fatigue were theones related to a lorry. Therefore the same hypothesis was accepted for bridges withmore than one slow lane. However it may happen that two lorries moving in two slowlanes in two opposite directions induce significant effects in case of long influence lines.A factor λ3 was then proposed :

λ ασ

σ3

5

15

1 5

1 1= + +ΛΝΜΜ

ΟΘΠΠ( )

/

L iΣ∆

∆

where L is the length of the considered influence line, α is a factor to be calibrated, ∆σiis the stress range in slow lane Nr. i.

Thus the calibration tests proved that it was possible to adjust the load characteristics ofFatigue Load Model 3 so that fatigue verifications could be carried out with rules similarto the rules used for the railway steel bridges. However these rules may not be given inEC1.3 : they shall be defined in Parts 2 of the structural Eurocodes for each type of

-54-

structure. Nevertheless, as one of the important factors is the annual number of heavyvehicles expected on the considered bridge, EC1.3 gives the following indications(Table V.2) :

Traffic categories Nobs per year and per slow lane

1 - Roads and motorways with 2 ormore lanes per direction with high flowrates of lorries

2,0 x 106

2 - Roads and motorways with mediumflow rates of lorries

0,5 x 106

3 - Main roads with low flow rates oflorries

0,125 x 106

4 - Local roads with low flow rates oflorries

0,05 x 106

Table V.2 - Number of lorries per year and per slow lane

On each fast lane, additionally, 10% of Nobs should be considered.

5.4 - FATIGUE LOAD MODELS 4 AND 5

Fatigue Load Models 4 and 5 are intended for damage calculations starting from thePalmgren-Miner law. Model 4 consists of a set of lorries with which it is deemed tosimulate a traffic model and Model 5 consists of the direct application of the recordedtraffic data.

5.4.1 Fatigue Load Model 4

It is made of the same set of lorries than Model 2, but with different load characteristicsthat are indicated in Figure 5.7. The equivalent axle loads corresponds to the averageloads taken from traffic records.

The stress range spectrum and the corresponding number of cycles due to the successivepassage of individual lorries, and without any other vehicle, should be used with anappropriate counting method (Rainflow or Reservoir method) to determine the fatiguedamage rate.

Concerning the local effects and when the vehicle transverse position is significant, astatistic distribution of this position should be considered according to the indications ofFigure 5.8.

-55-

Vehicle type Characteristics Percentage of heavyvehicles according to the

traffic typeAxle

spacing(m)

Axlefrequentload (kN)

Longdistance

Mediumdistance

Localtraffic

Type ofwheels

4.5 70130

20,0 50,0 AB

4.201.30

70120120

5,0 5,0 80,0 ABB

3.205.201.301.30

70150909090

40,0 20,0 5,0 ABCCC

3.406.001.80

701409090

25,0 15,0 5,0 ABBB

4.803.604.401.30

70130908080

10,0 10,0 5,0 ABCCC

Type ofwheels

Geometrical definition

A

B

C

Figure 5.7- Definition of the equivalent lorries ofFatigue Load Model 4

-56-

Figure 5.8

5.4.2 Fatigue Load Model 5

Fatigue Load Model 5 consists of the direct application of recorded traffic data,supplemented, if relevant, by appropriate statistical and projected extrapolations. Thismodel should be used only if supplementary rules are specified by the client. For moredetails, see Annex B of EC1.3.

-57-

ANNEX A

TO CHAPTER 2

TRAFFIC EFFECTS ON ROAD BRIDGESAND

TARGET VALUES

TABLES

-58-

L (m) V1Free

flowing

V12Free

flowing

V14Free

flowing

V124Free

flowing

V1234Free

flowing

V1Traffic

jam

V12Traffic

jam

V1234Traffic

jam

a)5

1020305075

100150200

565,3741,7

1004,01213,01560,01922,02240,02796,03285,0

751,4987,0

1293,01512,01837,02142,02387,02777,03090,0

1145,01250,01495,01720,02114,02543,02930,03620,04243,0

1051,01218,01502,01740,02141,02567,02943,03605,04192,0

988,41227,01560,01816,02221,02627,02972,03555,04054,0

477,8698,6

1096,01458,02133,02922,03672,05104,06475,0

889,01177,01803,02407,03556,04933,06265,08844,0

11350,0

916,31311,02013,02650,03823,05182,06468,08910,0

11240,0

b)5

1020305075

100150200

570,81145,02713,04741,0

10020,018640,029330,056430,090620,0

597,11583,04148,07245,0

14540,025140,036970,063420,092720,0

811,11867,04575,07914,0

16170,028960,044140,080810,0

125000,0

821,61887,05605,07953,0

16200,028960,044100,080530,0

124300,0

735,41911,04974,08710,0

17670,030990,046180,081120,0

121000,0

319,91014,03213,06313,0

14770,028990,046810,091930,0

148400,0

684,01578,04645,09237,0

22760,047440,080540,0

171300,0294200,0

682,91705,05085,0

10090,024710,051220,086570,0

183000,0312800,0

c)5

1020305075

100150200

127,8324,5824,3

1423,02833,04892,07211,0

12460,018380,0

155,8425,6

1141,02014,04077,07077,0

10420,017840,025980,0

237,4586,3

1442,02438,04716,07948,0

11500,019350,027970,0

225,0557,3

1382,02351,04594,07824,0

11410,019440,028380,0

212,5577,9

1515,02611,05072,08429,0

11950,019190,026520,0

112,0266,8732,5

1383,03184,06305,0

10330,020970,034900,0

203,7476,7

1277,02375,05368,0

10480,017020,034120,056270,0

201,3486,9

1331,02494,05681,0

11140,018140,036450,060230,0

d)5

1020305075

100150200

413,9945,0

2339,04098,08544,0

15600,024130,045160,070970,0

469,51246,03259,05679,0

11350,019540,028630,048810,071010,0

630,91617,04124,07119,0

14130,024290,035650,061140,089540,0

696,91672,04079,06932,0

13630,023450,034580,060040,089080,0

651,41628,04072,06964,0

13700,023430,034290,058680,085900,0

350,0803,6

2306,04517,0

10920,022510,037870,079700,0

135900,0

562,81350,03917,07680,0

18570,038180,064200,0

134800,0229500,0

609,71374,03983,07867,0

19240,039950,067650,0

143400,0245700,0

V1 : Lane n°1 (subjected to the heaviest load)V12 : Lane n°1 + Lane n°2V14 : Lane n°1 + Lane n°4 (sum of both heaviest lanes on both carriageways of themotorway)V124 : Lane n°1 + Lane n°2 + Lane n°4V1234 : All lanes of the motorway

Table A.1 : Effects of the recorded traffic on the A6 motorway

-59-

L (m) V1Free

flowing

V12Free

flowing

V14Free

flowing

V124Free

flowing

V1234Free

flowing

V1Traffic

jam

V12Traffic

jam

V1234Traffic

jam

e (< 0)5

1020305075

100150200

166,3204,7257,9298,4361,9424,9478,2567,5643,2

172,5218,9280,2325,0393,5459,4513,5602,5675,7

234,3285,6358,9415,5506,2597,6675,6808,7922,1

225,4289,0373,5435,9531,9624,8701,8828,2932,9

227,92909

374,9436,6531,5623,5699,3824,3927,9

136,9165,7218,2264,6346,1436,4518,9669,4807,4

194,4274,4383,4464,1587,6702,6801,9957,3

1082,0

237,7268,1333,1392,0496,3611,5715,8905,1

1078,0

e (> 0)5

1020305075

100150200

179,2193,9227,9258,8312,2369,8421,4512,6593,8

200,1234,6284,6323,1384,8446,7499,3588,5664,1

234,3310,0402,0463,3548,2621,2675,1753,8810,3

231,8319,7425,5494,2584,0654,7702,7763,0798,8

249,5325,3416,5477,3560,9632,7685,7763,1819,7

143,7149,1188,8229,9307,9398,3484,3646,3799,8

235,7257,1316,0372,2473,4586,7690,6881,3

1056,0

195,9280,5396,5481,8611,5734,5833,0990,4

1115,0

f (> 0)5

1020305075

100150200

352,9462,4597,0687,7815,4926,7

1012,01138,01233,0

417,7569,8762,1894,0

1081,01246,01370,01555,01691,0

1298,01864,02651,03014,03590,04017,04281,04564,04678,0

403,5485,5634,3764,9993,7

1247,01476,01895,02279,0

907,01206,01671,02059,02715,03421,04054,05188,06208,0

g (> 0)5

1015

430,7468,5492,4

435,5666,5855,4

568,1632,8673,8

525,4671,9776,0

365,3477,4557,9

V1 : Lane n°1 (subjected to the heaviest load)V12 : Lane n°1 + Lane n°2V14 : Lane n°1 + Lane n°4 (sum of both heaviest lanes on both carriageways of themotorway)V124 : Lane n°1 + Lane n°2 + Lane n°4V1234 : All lanes of the motorway

Table A.1 (following) : Effects of the recorded traffic on the A6 motorway

-60-

L (m) RN-V1Free flowing

RN-V1234Free

flowing

BR-V1Free

flowing

FN-V1Free

flowing

RN-V1Traffic

jam

RN-V1234Traffic jam

a)5

1020305075

100150200

443,5602,3826,7

1000,01278,01557,01796,02201,02548,0

878,51050,01287,01465,01743,02016,02246,02627,02948,0

837,2897,0

1088,01272,01605,01978,02320,02946,03521,0

390,8593,9886,2

1111,01461,01800,02077,02524,02883,0

390,4526,8799,4

1056,01541,02114,02664,03722,04742,0

673,9936,2

1415,01854,02664,03606,04500,06197,07818,0

b)5

1020305075

100150200

408,3908,3

2242,03950,08322,0

15370,024010,045580,072420,0

691,31869,04845,08277,0

15830,025890,036190,056860,077000,0

507,31299,03386,05982,0

12350,022080,033460,060390,092090,0

330,7846,6

2300,04222,09262,0

17530,027760,053550,085870,0

336,7728,0

2067,04048,09834,0

20320,034310,072510,0

124000,0

568,81423,04077,07867,0

18580,037460,062130,0

128000,0215100,0

c)5

1020305075

100150200

102,7257,4656,3

1143,02319,04090,06135,0

10910,016460,0

166,3461,3

1241,02177,04339,07380,0

10660,017630,024920,0

144,5373,6960,0

1663,03313,05705,08380,0

14380,021060,0

93,8227,1592,5

1068,02300,04298,06758,0

12920,020600,0

89,1213,9575,4

1066,02396,04646,07505,0

14920,024470,0

158,0378,0

1027,01920,04367,08563,0

13940,028000,046270,0

d)5

1020305075

100150200

313,4748,0

1889,03320,06902,0

12530,019260,035650,055540,0

502,91413,03805,06650,0

13090,021890,031090,049900,068600,0

404,11032,02708,04813,0

10050,018160,027760,050790,078260,0

273,9729,8

2002,03657,07911,0

14720,022970,043280,068110,0

271,8602,3

1711,03345,08090,0

16670,028080,059160,0

101000,0

455,71126,03256,06339,0

15160,030870,051580,0

107400,0181600,0

V1 : Lane n°1 (subjected to the heaviest load)V12 : Lane n°1 + Lane n°2V14 : Lane n°1 + Lane n°4 (sum of both heaviest lanes on both carriageways of themotorway)V124 : Lane n°1 + Lane n°2 + Lane n°4V1234 : All lanes of the motorway

For instance, the framed and shadowed values show that the effects of the trafficrecorded on the slow lane at Brohltal and at Fiano Romano are higher than the onesrecorded on the slow lane of the RN205. Besides, referring to the homologousvalues of table II.5, we notice that the values corresponding to the Brohltal location

-61-

are higher than the ones corresponding to the Auxerre location, and that these lastones are near the ones corresponding to the Fiano Romano location.

Table A.2 : Effects of various traffics

Lane 1 Span I1 I2 I3 Max(I4,I5) I6 I7 I8 I9

Envelope values(dynamic

magnificationincluded)

51020305075

100150200

695151333496860

12752237233732971820

115334

185383936

1423334857818522

1472521721

489111627644843

1087419145285175029174195

229245316375425463521618701

719963

1095132317012096244330503583

183313886

1247302554448294

1254219027

4981034264740339643

17124258103944360272

390969

241044909778

17415260823374347881

Mean values

51020305075

100150200

721138430696404

1136821010331835832789972

185383936

1423334857818522

1472521721

489111627644843

1087419145285175029174195

196218270320376421463545622

719920

1033118016742022234527963210

155289788

1088249945847167

1125916818

453911

252236118083

14693228743690055073

345856

194239488213

14316214762939342593

Table A.3 -a) : Envelope values and mean values for lane 1 - Free flowing traffic

Lane 1 Span I1 I2 I3 Max(I4,I5) I6 I7 I8 I9

Envelope values

51020305075

100150200

320101432136313

147703014352239

107954184831

112267732

138331846305

103302097034900

350803

23064517

10920225103787079700

135900

144166218265390475560765970

478840

1100153022603145403053656700

85233700

140036007397

126932654745407

285756

21884100

10787226963894881677

139909

247723

23954960

12360259224440595185

165017

Mean values

51020305075

100150200

320101429225651

142552970050450

101710170477

112267732

138331846305

103302097034900

350803

23064517

10920225103787079700

135900

144166207256346436522720915

478770

1098149421973034385152356588

85233679

136033656734

111822388639703

247711

22464757

11853248264240993980

163008

345856

194239488213

14316214762939342593

Table A.3 -b) : Envelope values and mean values for lane 1 - Congested traffic

-62-

Lane 1 Span I1 I2 I3 Max(I4,I5) I6 I7 I8 I9

Accepted"target" values

51020305075

100150200

695151333496860

142552970050450

101710170477

185383936

142333486305

103302097034900

489111627644843

10920225103787079700

135900

229245316375425463522720915

719963

1098149421973034385152356588

183313886

136033656734

111822388639703

4981034264740029906

204083450173651

124954

390969

24104757

11853248264240993980

163008

The bold italics values correspond to the free flowing traffic with dynamicmagnification

Table A.3 -c) : Accepted "target" values for lane 1

Lanes 1+2 Span I1 I2 I3 Max(I4,I5) I6 I7² I8 I9

Envelope values(dynamic

magnificationincluded)

51020305075

100150200

556210060207443788959550

103200200000

422472511575640740840

12012081358060388940

1548023614

47317402

1364425509407365177178600

30226234

1554028984462124296768225

Mean values

51020305075

100150200

51539084

15880289114533684963

150109

410470495567639728816

11881872322156828709

1534723507

27235494

1126219970307304158464912

345856

194239488213

14316214762939342593

Table A.4 -a)- Envelope values and mean values for lanes 1+2 - Free flowing traffic

-63-

Lanes 1+2 Span I1 I2 I3 Max(I4,I5) I6 I7 I8 I9

Envelope values5

1020305075

100150200

103720815387

10049240555097587824

144056243394

232590

149825875150

10179159463039048436

752171842527450

176943464556363

113509188063

302371469542658772869

10301318

102713481909242833574403537471818872

187481

128522674994

10216172533530259631

623159041967332

168413221053347

109340184611

534136540278329

189803926866756

120772210513

Mean values

51020305075

100150200

1037208148159013

217364369972764

135249223864

232590

149825875150

10179159463039048436

752171842527450

176943464556363

113509188063

302371399454556680797

10131270

102713481909242833574403537471818872

187481

1152208546709694

161673121949815

534136536647419

171093448857580

111522190711

345856

194239488213

14316214762939342593

Table A.4 -b) : Envelope values and mean values for lanes 1+2 - Congested traffic

Lanes 1+2 Span I1 I2 I3 Max(I4,I5)

I6 I7 I8 I9

Accepted"target" values

51020305075

100150200

103720815562

10060217364369972764

135249223864

232590

149825875150

10179159463039048436

752171842527450

176943464556363

113509188063

302371422472556680797

10131270

102713481909242833574403537471818872

187481

1201208546709694

161673121949815

623159047317402

15547304274947499961

165942

534136536647419

171093448857580

111522190711

The bold italics values correspond to the free flowing traffic with dynamic amplification

Table A.4 -c) : Accepted "target" values for lanes 1+2

-64-

Lanes 1+2+3 Span I1 I2 I3 Max(I4,I5) I6 I7 I8 I9

Envelope values(dynamic

magnificationincluded)

51020305075

100150200

125627387080

12933281275268185116

170984285723

331828

206035106862

12957198453665457154

95023295875

10197227724254566836

128036204945

376458572656789929

105312721571

155418102355288938604968600179309743

233660

183131906211

12289203484145969860

829219757549830

196303900064741

129863216818

669179252079767

214364096365804

139390240097

Mean values

51020305075

100150200

125627386825

11893269255194783899

164010267134

331828

206035106862

12957198453665457154

95023295875

10197227724254566836

128036204945

376458572623710815912

10591244

155418102355288938604968600179309743

233660

165029226210

11848185154145969860

829219757549040

193013660957684

129863216818

669179246909376

203834006965515

139390240097

Table A.5 -a) : Envelope values and mean values for lanes 1+2+3 - Mixed traffic

Lanes 1+2+3 Span I1 I2 I3 Max(I4,I5) I6 I7 I8 I9

Accepted"target" values

51020305075

100150200

125627386825

11893269255194783899

164010267134

331828

206035106862

12957198453665457154

95023295875

10197227724254566836

128036204945

376458572623710815912

10591244

155418102355288938604968600179309743

233660

165029226210

11848185154145969860

829219757549040

193013660957684

129863216818

669179246909376

203834006965515

139390240097

The bold italics values correspond to the free flowing traffic with dynamic amplification

Table A.5 -b) : Accepted "target" values for lanes 1+2+3

-65-

Lanes 1+2+3+4 Span I1 I2 I3 Max(I4,I5) I6 I7 I8 I9

Envelope values(dynamic

magnificationincluded)

51020305075

100150200

147433948772

158183452866804

109087179200292463

4311065262144328574

15735237444291865872

114729407498

12943278505044577309

142563221827

426563730842996

1129128414911825

20812272280133504364553266298680

10614

280837

237141047761

13289209944249671333

103328037348

12329231094240468031

133538222108

80122206421

11866254244917880906

142053244080

Mean values

51020305075

100150200

147433948772

14182308115810792851

168561272693

4311065262144328574

15735237444291865872

114729407498

12943278505044577309

142563221827

426563730755873

1005114814041722

20812272280133504364553266298680

10614

280837

237135217154

13036196464249671333

103328037348

10986220974085963740

133538222108

80122206421

10823235154556573948

142053244080

Table A.6 -a) : Envelope values and mean values for lanes 1+2+3+4 - Mixed traffic

Lanes 1+2+3+4 Span I1 I2 I3 Max(I4,I5) I6 I7 I8 I9

Accepted"target" values

51020305075

100150200

147433948772

14182308115810792851

168561272693

4311065262144328574

15735237444291865872

114729407498

12943278505044577309

142563221827

426563730755873

1005114814041722

20812272280133504364553266298680

10614

280837

237135217154

13036196464249671333

103328037348

10986220974085963740

133538222108

80122206421

10823235154556573948

142053244080

The bold italics values correspond to the free flowing traffic with dynamic amplification

Table A.6 -b) : Accepted "target" values for lanes 1+2+3+4

-66-

ANNEX B

TO CHAPTER 3

COMPARISON BETWEEN THEMAIN LODING SYSTEM EFFECTS

AND

THE TARGET VALUES

TABLE

(see 3.3.5)

-67-

Lane 1 Span I1 I2 I3 Max(I4,I5) I6 I7 I8 I9

"target"values

51020305075

100150200

695151333496860

142552970050450

101710170477

185383936

142333486305

103302097034900

489111627644843

10920225103787079700

135900

229245316375425463522720915

719963

1098149421973034385152356588

183313886

136033656734

111822388639703

4981034264740029906

204083450173651

124954

390969

24104757

11853248264240993980

163008

Modeleffects

51020305075

100150200

654165741707357

15757300544857098257

164820

180482

1231212543267840

121982344738071

497137334105959

12660240663884478522

131700

245298349389461548633803973

735870

1140141019502625330046506000

149364910

162235516909

113232331339523

517131032855768

12254232113733275066

125457

341897

24964763

11321233123952184596

146546Lanes1+2

Span I1 I2 I3 Max(I4,I5) I6 I7 I8 I9

"target"values

51020305075

100150200

103720815562

10060217364369972764

135249223864

232590

149825875150

10179159463039048436

752171842527450

176943464556363

113509188063

302371422472556680797

10131270

102713481909242833574403537471818872

187481

1201208546709694

161673121949815

623159047317402

15547304274947499961

165942

534136536647419

171093448857580

111522190711

Modeleffects

51020305075

100150200

105826316425

11081229814270767825

134231222200

294777

194733066554

11590177053317252952

803218452648987

184753420454240

107246177500

402483556609704815925

11431360

117213451690203527253587445061757900

241574

1385240850979670

155903147352746

838208550818727

179633314852376

102962169719

535136436346757

155863147052744

111462191743

Lanes1+2+3+4

Span I1 I2 I3 Max(I4,I5) I6 I7 I8 I9

"target"values

51020305075

100150200

147433948772

14182308115810792851

168561272693

4311065262144328574

15735237444291865872

114729407498

12943278505044577309

142563221827

426563730755873

1005114814041722

20812272280133504364553266298680

10614

280837

237135217154

13036196464249671333

103328037348

10986220974085963740

133538222108

80122206421

10823235154556573948

142053244080

Modeleffects

51020305075

100150200

127131657740

13365277655167182140

162765269640

353934

234239817902

13992213964014464143

96426276340

10838223204138265688

130045215400

482580669733848984

111713821646

141016202040246033004350540075009600

289691

167029076164

11710188963819064046

100725086120

10524216964009463414

124819205913

644164443918176

188913818664043

135443233092

-68-

Table B.1 : Comparison between the main loading system effects and the "target"values

-69-

ANNEX C

ELEMENTS FOR THE DEFINITIONOF BRIDGE CLASSES

-70-

C1 - ABOUT THE SITUATION TODAY

C1.1 Definition of the bridge classes in the various national regulations

Most of the national regulations directly define bridge classes or loading classes forbridges. But the criteria largely vary from one regulation to the other.

(1) For some of them the class definition is, for new bridges, related to the carriagewaywidth, that is supposed to be correlated with the traffic rate. For instance : the Fascicule61 Titre II of the French Ministry or the Swiss regulation (SIA 160).

a) In the French regulation three bridge classes are defined (Table C.I) :

Class Carriageway widthFirst classSecond classThird class

L ≥ 7 m5,50 m < L < 7,00 mL ≤ 5,50 m

Table C.I

For two loaded lanes the load reduction factor is given in Table C.II. Systems A and Bcare successively applied. System A becomes predominant when the spans are greaterthan about 30 m.

Loading system 1° class 2° class 3° classA(L) 1 0,77 0,628Bc 1 0,909 0,727

Table C.II

Actually the 2nd class is quite often used but the 3rd class is rarely needed (only forsmall local roads).

b) The class definition is more complicated in the Swiss regulation : in general areduction of the load model basic values is allowed (up to 25%) wherever thecarriageway is not wider than 6 m.

Besides, the intensity of the uniformly distributed load (except for the main lane wherethe concentrated loads act) has in any case different values for a carriageway widthsmaller than 9 m (3,5 kN/m2), between 9 and 13 m (3 kN/m2) and greater than 13 m (2,5kN/m2). However these variations correspond to load combinations on several lanes andnot to different types or intensities of traffic.

(2) Other regulations give the class definition as a function of the traffic capacity or ofthe expected traffic type on the considered road.

a) For instance in the German regulation (DIN 1072), two classes are defined (for thedesign of new bridges - other classes exist for the assessment of existing bridges, butthis is out of the scope of the Eurocode 1.3) :

-71-

- class 60/30 for motorways and national, regional and main local roads,- class 30/30 for small local roads.

The load variations between these two classes are linked to the reduction of the heavyvehicle total load on main lane, from 600 to 300 kN ; this one is identical to the one onthe second lane.

For instance the reduction factor of the total load on a two lanes deck of a simplysupported span and without hard strips is given in Table C.III :

Span length (m) Class 60/30 Class 30/3020 1 0,7650 1 0,89100 1 0,92

Table C.III

This table shows that the span length is a parameter related to the decreasing influenceof the concentrated loads. The reduction of load effect depends on the influence line ; itis about twice the one of the total load.

Actually, it seems that the class 30/30 is not of common use.

b) In the British Standard (BS 5400 et IRLS), the situation is more complicated. Usuallythe relevant authority chooses the bridge class from the chosen intensity of load systemHB (concentrated loads), corresponding to the expected traffic.

It has to be noticed that in the study file of the "Interim Design Standard" (long spanbridges loading), the intensity of the load defined in that norm "concerns bridgeslocated on heavy traffic commercial itineraries. A lighter capacity norm should likely bedefined for other bridges. An appropriate characteristic loading may stem from theexisting traffic data".

c) In the Italian regulation, three classes are conventionally defined. All footbridges arethe concern of the third one. The differences between classes 1 and 2 only concern, assame as in the German regulation, the intensity of the loads applied on the main lane.Thecompetent authority is here responsible for the bridge class definition in accordancewith the allowed vehicles load.

For instance the reduction factor between classes 1 and 2 is 0,83 for two lanes and 0,86for three lanes.

(3) The actual Danish regulation refers to the traffic and, as well, to the administrativeclassification of the road, with some limitations about the width.

-72-

C1.2 A few proposals

Some PT6 members proposed a few definitions of classes. They consist in the choice offactors α to be applied to the main loading system (Load Model 1).

(1) Pr. Bruls' proposal (Liège - November 1992)

Class α Q1 α Q2 α Q3 α q1

1. Normal class 1 1 1 12. Heavy class 1 1.5 3 13. Simplified class 1 1 0 14. Light class 0,8 0,8 0 0,85 Very light class 0,8 0,6 0 0,6

Table C.IV

Bridge classes refer to the traffic intensity and/or to its type (except for the simplifiedclass that rather corresponds to a "simplified method"). Nevertheless the trafficparameters are still to be specified in order a DAN could be arranged.

(2) Dr. Flint's proposal (December 1992)

Dr. Flint proposed the following classification, completed with the numerical values ofthe α factors.

Classes α Q1 α Q2 α Q3 α q1 α q2 α q3

Vehiclesload

Lorriesdensity

Flow rate.Traffic jamfrequency

1 Normal Normal High 1 1Normal 1 1

2 Normal High High 1,1 1,1Normal 1,1

3 Light Normal High 0,75 0,75Normal 0,75 0,40

4 Light High High 0,80 0,65Normal 0,80 0,65

Table C.V

In this proposal bridge classes should be defined as a function of several parametersrelated to types of traffic and of conditions. The term "Normal" refers to trafficconditions in continental Europe, with which the main model has been calibrated. It hasto be noticed that some values of α (0,75) are not in accordance with the rules given inEC1.3 (αQ1 ≥ 0,8). In all cases the classification criteria in light, normal and high arestill to be defined.

-73-

(3) Work hypothesis in Denmark (May 1993)

The actual Danish regulation distinguishes several bridge classes :

- a class for motorways and main roads, including all the bridges supposed to supporta heavy and dense traffic ; for these bridges, all the α factors will probably be equalto 1 ;

- a class for public or private roads with two lanes maximum, and that are supposedto support light traffic only ; for these bridges the considered values of the α factorsare :

α α α α αQ Q q q qr1 2 1 20 8 0 5 1= = = = =, ,

- a class for public or private roads with one single lane and supporting vehicles oflimited weight (with the appropriate road signs), but that may cross public areas ;for these bridges on which the crossing of a 48 tons 6-axle lorry is allowed at lowspeed, the considered values for α are :

α α αQ1 q1 qr = 0.5 ; = 0.5 ; (?) = 1

C1.3 Explanation of the problem

The class definition may be tackled in three successive steps :a) characterisation of a road traffic ;b) definition of traffic classes and, therefore, of bridge classes ;c) definition of the α factors for these classes.

Below we will only deal with the problem of the choice of characteristic values.However, in some cases, the design values (γ factors) or other representative values (ψfactors) might be modified as well.

A road traffic characterisation is not easy because it depends on many parameters,especially the number of heavy vehicles per lane and per year, the average load of thesevehicles, the traffic jam frequency, etc. It should be useful, for the designers or thecompetent authorities, to keep only a few parameters (not more than three).

Concerning the second point it seems that the bridge class definition must be related to :- the carriageway width (a bridge to be erected with a carriageway width below 6 m

should not be taken as a first class bridge) ;- the expected traffic (type and intensity).

C2. - ROAD TRAFFIC CHARACTERISATION

(1) The road traffic characterisation should be limited to the traffic which effects aresimulated by the main loading system (Load Model 1) and the single axle system (LoadModel 2).

-74-

Besides it should only refer to the part of traffic that induces most of the effects, thatmeans inducing effects close to the effects produced by the characteristic loads. Theproperties of this part of traffic are not a priori the same than the ones that induce themain fatigue effects.

(2) The main parameters that characterise a traffic are :- its composition, for instance the percentage of lorries1,-its density, for instance the average number of vehicles per year or the annual

average of the vehicle number per day1,- its conditions, for instance the traffic jam frequency2,- the extreme loads of the vehicles and of their axles32 ,- and, if relevant, the influence of the road signs to be placed.

Each of these parameters may be quantified, but with some uncertainty ; however, thebiggest difficulty is to combine them in order to define the traffic classes.

It appears as well that a preliminary distinction shall be done between uni- and bi-directional traffic. This distinction may be taken as known for a particular project, if theconsidered authority is supposed to control any transient situation.

(3) The percentage of lorries (vehicles heavier than 3,5 t), in annual average value,varies between 0,1 and 0,25 for most of the roads. Table C.VI gives some informationconcerning the traffics used for the set up of the EC1.3 models.

1 May these exemples be taken as definitions? Are other concepts necessary? Is the term "intensity" a clearconcept? Answers to these questions shall be given in relation with the similar questions concerning thetraffic characterisation for the fatigue.

2 See the previous note.3 To be characterise with the total load of a vehicle or of an axle, associated to an exceeding probability in

100 years equal to 0,10 (which gives respectivly 900 kN and 270 kN for the Auxerre traffic).

-75-

Situation Road type(number oflanes for the

records)

Lorrypercentage

Percentage relatedto the vehicles

category1)

Average valueof the lorry

maximum loadper day (kN)

Cl.I Cl.II

Cl.III

Cl.IV

Auxerre (F)(correspondingto α = 1)

Motorway(1 lane)

32 % 22.7 1.3 65.2 10.8 630

Angers (F)(bi-directional, 2lanes)

National road(1 lane)

17% 26.7 2.5 59.9 10.9 490

Chamonix (F)(bi-directional, 2lanes)

Main road withlong distancetraffic (1 lane)

32% 14.4 6.4 66.9 12.3 570

Fiano Romano(I)

Motorway(1 lane)

47% 41.4 7.0 29.0 22.6 590

Brohltal (D) Motorway(1 lane)

43% 16.6 1.6 40.2 41.6 650

Forth (GB) Motorway(1 lane)

26% 52.3 14.5 33.2 0.0 400

(1) The lorry categories are defined below :- Category I : single vehicle with two axles- Category II : single vehicle with more than two axles- Category III : articulated vehicle- Category IV : vehicle with trailer

Table C.VI

On main roads on which the traffic rate is high (for instance more than 2000 veh./d.),variations of the percentage due to local reasons are not expected during the bridgelifetime. This may be wrong for roads with low traffic rate.It has to be considered that the lorry percentage may vary sensibly within a day,according to the considered period.

(4) Traffic rate to be taken into account shall be the expected rate at a time as far as theextrapolations can go, that means around the year 2010.

By reference to some French rules a relation may be established between thecarriageway width (without hard strips) and the associated normal country traffic, inannual average value of the number of veh./d.

w (m) Traffic rate (d)5,50 d ≤ 500 (bi-directional) or d ≤ 1 500 (uni-directional)6,00 500 ≤ d ≤ 2 000 (bi-directional) or 1 500 ≤ d ≤ 6 000 (uni-directional)7,00 2 000 ≤ d ≤ 8 000 (bi-directional) or 6 000 ≤ d ≤ 20 000 (uni-directional)

10,50 8 000 ≤ d ≤ 12 000 (bi-directional) or d > 20 000 (uni-directional)2x7,00 12 000 ≤ d ≤ 40 000 (for both directions)

2 x 10.50 40 000 ≤ d

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Table C.VII

To give an idea, the vehicle speed is progressively decreased by the other vehicles whenthe medium values of these ranges are reached, and traffic jams often occur when thelimits of these ranges are exceeded of 20% or more.

(5) Traffic jam frequency may be caused by :

- an exceeding, by traffic rate, of the upper values of the ranges given in Table C.VII ;however these values should not be considered as normal design hypotheses ;

- or by local situations that do not depend on the bridge, for instance traffic lights orcross-roads near the bridge.

Usually, except for particular situations (transient situations, controlled traffic,accidental situations) and in some town areas, the frequency of simultaneous traffic jamsin both directions is a lot smaller than for a single direction (10 to 100 times less).

The traffic jam frequency shall naturally be taken into account for long span bridges. Itis not significant for small bridges or small structure elements.

The expected frequency of traffic jam in one direction may thus be taken into account ifsome values of the αq factors are fixed without touching the αQ factors.

For bi-directional bridges, the small frequency of traffic jam in both directions issupposed to be taken into account in Load Model 1 that considers one single notionallane Nr. 1.

(6) The extreme loads of vehicles and axles cannot be easily identified for individualbridges, except for bridges located on some itineraries where traffic conditions are verybad, for instance on roads with a 15% (or more) slope.

That is the reason why EC1.3 specifies that the factor αQ1 shall not be less than 0,8 ,and the value 0,9 was considered for small roads. It results from a combination of a lowdensity and of a rather favourable distribution of the individual loads.

Nevertheless it seems right to reconsider some extreme vehicle loads in some countries.In that goal the statistical data used for the set up of Load Models 1 and 2 of EC1.3 maybe compared with the national statistical data. The αQ1 factor (for which the extremeload seems to be the significant parameter), but as well the αq1 factor and maybe the αQ2 factor should probably be revised according to the comparison results. The lorrymaximum load is not directly related to the other parameters : for instance we may finda low circulation density but with very heavy vehicles.

(7) We shall consider as well if other parameters are not relevant to define the bridgeclasses4. For instance, have the traffic scenarios used in EC1.3 to be reconsidered ?

4 In a contribution, Pr. Sanpaolesi and M. Croce drew up a more complete list : the maximum expectedload of lorries, the average expected load of lorries, the expected traffic rate, the expected lorriespercentage, the traffic jam rate, the bridge width, the bridge length and/or the bridge erection cost, the

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Shall exceptional scenarios leading to vehicle accumulation be considered ? In order toget an easier evaluation, examples of actual vehicles that induce similar effects to theones with the main loading model (with α factors equal to 1 and dynamic overvaluationscorresponding to the indicated flow conditions) are given in Figures C.1 to C.4. Wehave to keep in mind that the characteristic loads shall not lead to exceeding of theelasticity limit and shall therefore correspond to a rather low exceeding probability on aparticular bridge during its life-time.

In Figures C.1 to C.4 the safety distances between vehicles (that depend on their speed)have been taken into account. That is the reason why two lorries of 770 kN are on laneNr. 1 when the speed is 20 km/h whereas the configuration is different with a 5 km/hspeed as the vehicles are closer to each other. Besides, light vehicles are not represented.

Figure C.1

bridge location, the expected traffic evolution during the exploitation duration, the expected evolution ofthe road network. For some of these factors the data that can be numerically quantified should be moreprecisely identified as parameters, while the others should be classified (for instance is it possible andsatisfactory to identify the industrial and/or town areas to characterise a bridge location ?).

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Figure C.2

Figure C.3

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Figure C.4

The parameters describing the traffic in a significant way shall probably be different forthe effects caused by a single vehicle and for the effects caused by a group of vehicles.The first ones mostly influence the αQ factors while the other ones influence the αqfactors. For instance the average lorry load, the lorry percentage and the traffic jam rateshall strongly influence the αq factors.

Actually some parameters that specifically characterise the fatigue effects (especially thepercentage of different types of lorries) do not seem to be considered as significant forthe characteristic values.

Sometimes some parameters may be directly taken into account. In other cases they mayeasily be substituted by other parameters or criteria that are correlated to them and thatare easier to get. For instance town traffic, traffic of medium or long distance, may betaken into account to replace other parameters ; same thing for some road and streetclassifications.

The carriageway length may as well, as indicated before, be taken into account for newstructures to be related to evaluations of traffic rate.

C3. - DEFINITION OF TRAFFIC CLASSES

As said above the parameters that act upon the local and general effects are sensiblydifferent. Therefore a class identification that globally covers all the aspects seems to bea complicated (and even dubious) work. The best approach is probably to identify andto separately consider the most significant parameters for the various α factors.

In that approach it seems that a differentiation of the αq1 factor is particularlyinteresting. The problem should not be complicated to solve because its numeral valueshould only depend on a limited number of vehicles. However this group of vehicles andits statistical properties depend on the total traffic (even if the records are done on onelane only). That is the reason why, for instance, the traffic parameters shall distinguish ifthe roads and streets are uni- or bi-directional.

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Actually the exceptional bridges (very long loaded lengths) should probably not beincluded in the first definition of classes.It may be useful to know which are the other α factors that are of some interest in eachcountry.

C4. - DEFINITION (CHOICE) OF THE αααα FACTORS

In order that the problem be not getting more complicated we assume below that thechoice of the α factors will lead to proportional effects acting on all the representativeand project values, which means that in each country the values of the γ and ψ factorswill be the same for all classes.

However it seems rational that a country prefer to modify only a few values of thesefactors because they are supposed to have a significant influence on the projects in thiscountry. In such a case the content of the structural Eurocodes (Parts 2) shall beconsidered together with the traffic data.

Besides some group of vehicles may be accidental in some countries, which means thatsuch a situation will only be covered by the ultimate limit states verifications, withreduced safety factors. This could be an example of socio-economical decision based ontechnical data, and not only a technical decision. This may have a non inconsiderableeffect on the numerical values. On the opposite side and because of the weak scatter ofthe maximum loads during a given time interval for a given traffic scenario, to keep thesame fractiles may induce significant numerical consequences on the ψ factor values.